Torsion for Homological Complexes of Nonassociative Algebras with Metagroup Relations

Lüdkovsky, S. V.

doi:10.3390/axioms10040319

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…Proof. An existence of φ satisfying condition (23) follows from identities (16)- (22). Similarly, there exists a G-graded homomorphism η : C → C such that η(x⊗ y) = x ⊗ y for each x ∈ X and y ∈ Y.…”

Section: Modules Over Nonassociative Algebras With Metagroup Relationsmentioning

confidence: 93%

“…Therefore, it is important to develop this area over octonions, Cayley-Dickson algebras, and more general nonassociative algebras with metagroup relations. Examples of nonassociative algebras, modules, and homological complexes with metagroup relations are given in [12,13,23]. In these works, it is shown that generalized Cayley-Dickson algebras are particular cases of metagroup algebras.…”

Section: Introductionmentioning

confidence: 99%

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Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations

Lüdkovsky

2022

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A class of nonassociative algebras is investigated with mild relations induced from metagroup structures. Modules over nonassociative algebras are studied. For a class of modules over nonassociative algebras, their extensions and splitting extensions are scrutinized. For this purpose tensor products of modules and induced modules over nonassociative algebras are investigated. Moreover, a developed cohomology theory on them is used.

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Section: Modules Over Nonassociative Algebras With Metagroup Relationsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations

Lüdkovsky

2022

Axioms

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On Cohomology of Simple Modules for Modular Classical Lie Algebras

Ibraev

Kainbaeva

Menlikozhaeva

2022

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In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic p > h, where h is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras of semisimple and simply connected algebraic groups. To describe the cohomology of simple modules, we will use the properties of the connections between ordinary and restricted cohomology of restricted Lie algebras.

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Satellites of Functors for Nonassociative Algebras with Metagroup Relations

Lüdkovsky

2022

Mathematics

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Torsion for Homological Complexes of Nonassociative Algebras with Metagroup Relations

Abstract: The article is devoted to homological complexes and modules over nonassociative algebras with metagroup relations. Smashed tensor products of them are studied. Their torsions and homomorphisms are investigated.

Cited by 5 publications

References 25 publications

Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations

Splitting Extensions of Nonassociative Algebras and Modules with Metagroup Relations

On Cohomology of Simple Modules for Modular Classical Lie Algebras

Satellites of Functors for Nonassociative Algebras with Metagroup Relations

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