列对

Q3 Mathematics

Communications in Mathematics Pub Date : 2024-01-03 DOI:10.46298/cm.12413

Letterio Gatto, Louis Rowen

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引用次数: 0

摘要

通过对系统理论的扩展，我们引入了一种列半代数 "对 "的理论，它与经典的列代数理论相似，只是用一个 "空集 "代替了 $0$。本文列举了一些例子。除了通用代数定义之外，这些列对还包含两个范畴，一个是保留空和的 "弱列态式"，另一个是保留取代相等的超越关系$\preceq$的"$\preceq$态式"。我们提供了这三个范畴的 PBW（Poincare-Birkhoff-Witt）定理的版本。

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Lie pairs

Extending the theory of systems, we introduce a theory of Lie semialgebra ``pairs'' which parallels the classical theory of Lie algebras, but with a ``null set'' replacing $0$. A selection of examples is given. These Lie pairs comprise two categories in addition to the universal algebraic definition, one with ``weak Lie morphisms'' preserving null sums, and the other with ``$\preceq$-morphisms'' preserving a surpassing relation $\preceq$ that replaces equality. We provide versions of the PBW (Poincare-Birkhoff-Witt) Theorem in these three categories.

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来源期刊

Communications in Mathematics Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

45 weeks

期刊介绍： Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.