Invariants of Lie Algebras Extended Over Commutative Algebras Without Unit

Зусманович, Паша

doi:10.1142/s1402925110000817

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2021

2022

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Cited by 7 publications

(1 citation statement)

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“…Unfortunately, such calculations, performed up to certain degree in generators, are not conclusive if not supported by cohomological arguments of the type elucidated in [9]: there might be some relations of higher degree left unobserved.…”

Section: Introductionmentioning

confidence: 98%

Defining Relations of Almost Affine (Hyperbolic) Lie Superalgebras

Bouarroudj¹,

Grozman²,

Leites³

2021

JNMP

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Section: Introductionmentioning

confidence: 98%

Defining Relations of Almost Affine (Hyperbolic) Lie Superalgebras

Bouarroudj¹,

Grozman²,

Leites³

2021

JNMP

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A Compendium of Lie Structures on Tensor Products

Зусманович

2014

J Math Sci

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Abstract. We demonstrate how a simple linear-algebraic technique used earlier to compute low-degree cohomology of current Lie algebras, can be utilized to compute other kinds of structures on such Lie algebras, and discuss further generalizations, applications, and related questions. While doing so, we touch upon such seemingly diverse topics as associative algebras of infinite representation type, Hom-Lie structures, Poisson brackets of hydrodynamic type, Novikov algebras, simple Lie algebras in small characteristics, and Koszul dual operads.

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On δ-derivations of Lie algebras and superalgebras

Зусманович

2010

Journal of Algebra

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Witt algebra Current Lie algebra Non-semigroup grading Grassmann envelope We study δ-derivations -a construction simultaneously generalizing derivations and centroid. First, we compute δ-derivations of current Lie algebras and of modular Zassenhaus algebra. This enables us to provide examples of Lie algebras having 1 2 -derivations which are divisors of zero, thus answering negatively a question of Filippov. Second, we note that δ-derivations allow, in some circumstances, to construct examples of non-semigroup gradings of Lie algebras, in addition to the recent ones discovered by Elduque. Third, we note that utilizing the construction of the Grassmann envelope allows to obtain results about δ-(super)derivations of Lie superalgebras from the corresponding results about Lie algebras. In this way, we prove that prime Lie superalgebras do not possess nontrivial δ-(super)derivations, generalizing the recent result of Kaygorodov.

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Invariants of Lie Algebras Extended Over Commutative Algebras Without Unit

Cited by 7 publications

References 23 publications

Defining Relations of Almost Affine (Hyperbolic) Lie Superalgebras

Defining Relations of Almost Affine (Hyperbolic) Lie Superalgebras

A Compendium of Lie Structures on Tensor Products

On δ-derivations of Lie algebras and superalgebras

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