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2-Local derivations on the W-algebra W(2,2) W-代数W(2,2)的2-局部导数
arXiv: Rings and Algebras Pub Date : 2020-03-12 DOI: 10.1142/s0219498821502376
Xiaomin Tang
{"title":"2-Local derivations on the W-algebra W(2,2)","authors":"Xiaomin Tang","doi":"10.1142/s0219498821502376","DOIUrl":"https://doi.org/10.1142/s0219498821502376","url":null,"abstract":"The present paper is devoted to study 2-local derivations on W-algebra $W(2,2)$ which is an infinite-dimensional Lie algebras with some out derivations. We prove that all 2-local derivations on the W-algebra $W(2,2)$ are derivation. We also give a complete classification of the 2-local derivation on the so called thin Lie algebra and prove that it admits a lots of 2-local derivations which are not derivations.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130675606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Hamming spaces and locally matrix algebras 汉明空间与局部矩阵代数
arXiv: Rings and Algebras Pub Date : 2020-03-01 DOI: 10.1142/s0219498821501474
O. Bezushchak, B. Oliynyk
{"title":"Hamming spaces and locally matrix algebras","authors":"O. Bezushchak, B. Oliynyk","doi":"10.1142/s0219498821501474","DOIUrl":"https://doi.org/10.1142/s0219498821501474","url":null,"abstract":"We introduce an abstract definition of a Hamming space that generalizes standard Hamming spaces $( mathbb{Z}/ 2 mathbb{Z})^n $. We classify countable locally standard Hamming spaces and show that each of them can be realized as the Boolean algebra of idempotents of a Cartan subalgebra of a locally matrix algebra.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128767086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Nilpotent Lie algebras of derivations with the center of small corank 以小圆角为中心的幂零李代数
arXiv: Rings and Algebras Pub Date : 2020-02-24 DOI: 10.15330/cmp.12.1.189-198
Y. Chapovskyi, L. Mashchenko, A. Petravchuk
{"title":"Nilpotent Lie algebras of derivations with the center of small corank","authors":"Y. Chapovskyi, L. Mashchenko, A. Petravchuk","doi":"10.15330/cmp.12.1.189-198","DOIUrl":"https://doi.org/10.15330/cmp.12.1.189-198","url":null,"abstract":"Let $mathbb K$ be a field of characteristic zero, $A$ an integral domain over $mathbb K$ with the field of fractions $R = text{Frac}(A),$ and $text{Der}_{mathbb{K}}A$ the Lie algebra of all $mathbb K$-derivations on $A$. \u0000Let $W(A):=Rtext{Der}_{mathbb{K}} A$ and $L$ a nilpotent subalgebra of rank $n$ over $R$ of the Lie algebra $W(A).$ We prove that if the center $Z=Z(L)$ is of rank $geq n-2$ over $R$ and $F=F(L)$ is the field of constants for $L$ in $R,$ then the Lie algebra $FL$ is contained in a locally nilpotent subalgebra of $ W(A)$ of rank $n$ over $R$ with a natural basis over the field $R.$ It is also also proved that the Lie algebra $FL$ can be isomorphically embedded (as an abstract Lie algebra) into the triangular Lie algebra $u_n(F)$ which was studied early by other authors.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"284 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122965361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strongly graded Leavitt path algebras 强分级莱维特路径代数
arXiv: Rings and Algebras Pub Date : 2020-02-17 DOI: 10.1142/S0219498822501419
Patrik Nystedt, Johan Oinert
{"title":"Strongly graded Leavitt path algebras","authors":"Patrik Nystedt, Johan Oinert","doi":"10.1142/S0219498822501419","DOIUrl":"https://doi.org/10.1142/S0219498822501419","url":null,"abstract":"Let $R$ be a unital ring, let $E$ be a directed graph and recall that the Leavitt path algebra $L_R(E)$ carries a natural $mathbb{Z}$-gradation. We show that $L_R(E)$ is strongly $mathbb{Z}$-graded if and only if $E$ is row-finite, has no sink, and satisfies Condition (Y). Our result generalizes a recent result by Clark, Hazrat and Rigby, and the proof is short and self-contained.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"193 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122509494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Morita equivalent unital locally matrix algebras 森田等效单位局部矩阵代数
arXiv: Rings and Algebras Pub Date : 2020-02-17 DOI: 10.12958/adm1545
O. Bezushchak, B. Oliynyk
{"title":"Morita equivalent unital locally matrix algebras","authors":"O. Bezushchak, B. Oliynyk","doi":"10.12958/adm1545","DOIUrl":"https://doi.org/10.12958/adm1545","url":null,"abstract":"We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally connected. For an arbitrary uncountable dimension $alpha$ and an arbitrary not locally finite Steinitz number $s$ there exist unital locally matrix algebras $A$, $B$ such that $dim_{F}A=dim_{F}B=alpha$, $mathbf{st}(A)=mathbf{st}(B)=s$, however, the algebras $A$, $B$ are not Morita equivalent.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116266090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras Rota-Baxter代数、树形代数和Pre-Lie代数的匹配集
arXiv: Rings and Algebras Pub Date : 2020-02-12 DOI: 10.1155/2020/9792726
Dan Chen, Xiao-song Peng, Chia Zargeh, Yi Zhang
{"title":"Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras","authors":"Dan Chen, Xiao-song Peng, Chia Zargeh, Yi Zhang","doi":"10.1155/2020/9792726","DOIUrl":"https://doi.org/10.1155/2020/9792726","url":null,"abstract":"In this paper, we introduce the Hom-algebra setting of the notions of matching Rota-Baxter algebras, matching (tri)dendriform algebras and matching (pre)Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom-algebraic structures.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133387432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Local and 2-Local Derivations of Locally Simple Lie Algebras 局部简单李代数的局部和2-局部导数
arXiv: Rings and Algebras Pub Date : 2020-02-03 DOI: 10.22363/2413-3639-2022-68-1-95-109
Sh. A. Ayupov, K. Kudaybergenov, B. Yusupov
{"title":"Local and 2-Local Derivations of Locally Simple Lie Algebras","authors":"Sh. A. Ayupov, K. Kudaybergenov, B. Yusupov","doi":"10.22363/2413-3639-2022-68-1-95-109","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-68-1-95-109","url":null,"abstract":"In the present paper we study local and 2-local derivations of locally finite split simple Lie algebras. Namely, we show that every local and 2-local derivation on such Lie algebra is a derivation.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122352303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
f-Biderivations and Jordan biderivations of unital algebras with idempotents 幂等一元代数的f-双推导和Jordan双推导
arXiv: Rings and Algebras Pub Date : 2020-01-25 DOI: 10.1142/s0219498821500821
M. A. Bahmani, D. Bennis, H. R. E. Vishki, B. Fahid
{"title":"f-Biderivations and Jordan biderivations of unital algebras with idempotents","authors":"M. A. Bahmani, D. Bennis, H. R. E. Vishki, B. Fahid","doi":"10.1142/s0219498821500821","DOIUrl":"https://doi.org/10.1142/s0219498821500821","url":null,"abstract":"The notion of f-derivations was introduced by Beidar and Fong to unify several kinds of linear maps including derivations, Lie derivations and Jordan derivations. In this paper we introduce the notion of f-biderivations as a natural \"biderivation\" counterpart of the notion of \"f-derivations\". We first show, under some conditions, that any f-derivation is a Jordan biderivation. Then, we turn to study f-biderivations of a unital algebra with an idempotent. Our second main result shows, under some conditions, that every Jordan biderivation can be written as a sum of a biderivation, an antibiderivation and an extremal biderivation. As a consequence we show that every Jordan biderivation on a triangular algebra is a biderivation.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130223679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Context-Free Languages and Associative Algebras with Algebraic Hilbert Series 具有代数希尔伯特级数的上下文无关语言和关联代数
arXiv: Rings and Algebras Pub Date : 2020-01-24 DOI: 10.1007/978-3-030-63111-6_14
R. L. Scala, D. Piontkovski
{"title":"Context-Free Languages and Associative Algebras with Algebraic Hilbert Series","authors":"R. L. Scala, D. Piontkovski","doi":"10.1007/978-3-030-63111-6_14","DOIUrl":"https://doi.org/10.1007/978-3-030-63111-6_14","url":null,"abstract":"","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122947984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Outer derivations of complex solvable Lie algebras with the nilradical of maximal rank 具有极大秩零根的复可解李代数的外导
arXiv: Rings and Algebras Pub Date : 2020-01-18 DOI: 10.29229/uzmj.2020-4-5
K. Abdurasulov, R. Q. Gaybullayev
{"title":"Outer derivations of complex solvable Lie algebras with the nilradical of maximal rank","authors":"K. Abdurasulov, R. Q. Gaybullayev","doi":"10.29229/uzmj.2020-4-5","DOIUrl":"https://doi.org/10.29229/uzmj.2020-4-5","url":null,"abstract":"In the present paper we prove the existence outer derivations finite-dimensional solvable Lie algebras with nilradical of maximal rank and complementary subspace to nilardical of dimension less than rank of the nilradical.","PeriodicalId":233322,"journal":{"name":"arXiv: Rings and Algebras","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126087661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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