约旦上代数和相关列上代数的循环同源性

arXiv - MATH - Rings and Algebras Pub Date : 2024-09-05 DOI:arxiv-2409.03726

Consuelo Martínez, Efim Zelmanov, Zezhou Zhang

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摘要

我们研究了约旦超基团的循环同调与其 Tits-Kantor-Koecher Lie 超基团的第二同调之间的关系。特别是，我们把重点放在了作为带状代数的康托双倍的乔丹超代数上。我们将所得结果应用于计算任意系数环上的哈密顿和接触型李超拉的第二同调和普遍中心扩展。

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Cyclic homology of Jordan superalgebras and related Lie superalgebras

We study the relationship between cyclic homology of Jordan superalgebras and second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of bracket algebras. The obtained results are applied to computation of second cohomologies and universal central extensions of Hamiltonian and contact type Lie superalgebras over arbitrary rings of coefficients.

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arXiv - MATH - Rings and Algebras

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