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Titlebook: Algebraic Structures and Applications; SPAS 2017, Västerås Sergei Silvestrov,Anatoliy Malyarenko,Milica Ranči Conference proceedings 2020

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Algebras with Ternary Composition Law Combining , and , Gradings, . and ., satisfying quadratic and cubic relations respectively, . and ., .. Differential calculus of the first order is defined on these algebras, and its fundamental properties investigated. The invariance properties of the generalized algebras are also considered.
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Classification of Low-Dimensional Hom-Lie Algebras, linear endomorphism constructed upto isomorphism together with non-isomorphic canonical representatives for all the families in that case. We further give a list of 4-dimensional Hom-Lie algebras arising from a general nilpotent linear endomorphisms.
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A Review on Hom-Gerstenhaber Algebras and Hom-Lie Algebroids,uss about representations and cohomology of Hom-Lie algebroids that yields a differential calculus and dual description for Hom-Lie algebroids. Later on, we summarise the relationship between Hom-Lie algebroids and Hom-Gerstenhaber algebras.
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