Abstract
The article is devoted to homological complexes. Smashly graded modules and complexes are studied over nonassociative algebras with metagroup relations. Smashed tensor products of homological complexes are investigated. Their homotopisms and homologisms are scrutinized.
Highlights
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For some nonassociative algebrashomology theory was studied such as Lie algebras, pre-Lie algebras, flexible algebras, alternative algebras
Graded modules and complexes are studied over nonassociative algebras with metagroup relations
Summary
The generalized Cayley–Dickson algebras from a large class are utilized in algebraic geometry and in mathematical analysis, partial differential equations (PDEs), physics of elementary particles, theory of operators and founded applications in natural sciences including physics and quantum field theory (see [7,8,10,12,13,14]) For some nonassociative algebras (co)homology theory was studied such as Lie algebras, pre-Lie algebras, flexible algebras, alternative algebras (see, for example, [3,24,25,26]) Structures of the latter algebras are quite different from that of the generalized Cayley–Dickson algebras and the nonassociative algebras with metagroup relations.
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