Non-commutative Hom-Poisson algebras
Donald Yau
TL;DR
This paper introduces non-commutative Hom-Poisson algebras, a Hom-type generalization of non-commutative Poisson algebras, exploring their properties, constructions, and equivalences.
Contribution
It develops the theory of non-commutative Hom-Poisson algebras, including their closure properties, tensor product behavior, and the equivalence with admissible Hom-Poisson algebras.
Findings
Hom-Poisson algebras are closed under twisting by suitable self-maps.
Hom-Poisson algebras with commutative Hom-associative product are closed under tensor products.
Multiplicative admissible Hom-Poisson algebras are Hom-power associative.
Abstract
A Hom-type generalization of non-commutative Poisson algebras, called non-commutative Hom-Poisson algebras, are studied. They are closed under twisting by suitable self-maps. Hom-Poisson algebras, in which the Hom-associative product is commutative, are closed under tensor products. Through (de)polarization Hom-Poisson algebras are equivalent to admissible Hom-Poisson algebras, each of which has only one binary operation. Multiplicative admissible Hom-Poisson algebras are Hom-power associative.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology