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Abstract. Let B be a commutative algebra and A be a B-algebra (determined by an algebra homomorphism ε : B → A). M. D. Staic introduced a Hochschild like cohomology… Click to show full abstract
Abstract. Let B be a commutative algebra and A be a B-algebra (determined by an algebra homomorphism ε : B → A). M. D. Staic introduced a Hochschild like cohomology H((A,B, ε);A) called secondary Hochschild cohomology, to describe the non-trivial B-algebra deformations of A. J. Laubacher et al later obtained a natural construction of a new chain (and cochain) complex C•(A,B, ε) (resp. C • (A,B, ε)) in the process of introducing the secondary cyclic (co)homology. It turns out that unlike the classical case of associative algebras (over a field), there exist different (co)chain complexes for the B-algebra A. In this paper, we establish a connection between the two (co)homology theories for B-algebra A. We show that the pair (
Journal Title: Communications in Algebra
Year Published: 2021
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