一对相容李括号的全称包络代数

Int. J. Algebra Comput. Pub Date : 2021-10-13 DOI:10.1142/S0218196722500588

V. Gubarev

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引用次数: 0

摘要

利用poincarei - birkhoff - witt性质和Groebner-Shirshov基技术，我们找到了一对相容Lie括号的V. Ginzburg和M. Kapranov意义上的关联泛包络代数的线性基。我们证明了在n维相容李代数上这个包络的增长率等于n+1。

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Universal enveloping algebra of a pair of compatible Lie brackets

Applying the Poincare-Birkhoff-Witt property and the Groebner-Shirshov bases technique, we find the linear basis of the associative universal enveloping algebra in the sense of V. Ginzburg and M. Kapranov of a pair of compatible Lie brackets. We state that the growth rate of this universal enveloping over $n$-dimensional compatible Lie algebra equals $n+1$.

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来源期刊

Int. J. Algebra Comput.

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