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1.	Börjeson, Kaj, 1989- (författare) A Algebras Derived from Associative Algebras with a Non-Derivation Differential 2015 Ingår i: Journal of Generalized Lie Theory and Applications. - : OMICS Publishing Group. - 1736-5279 .- 1736-4337. ; 9:1 Tidskriftsartikel (refereegranskat)abstract Given an associative graded algebra equipped with a degree +1 differential delta we define an A∞-structure that measures the failure of delta to be a derivation. This can be seen as a non-commutative analog of generalized BV-algebras. In that spirit we introduce a notion of associative order for the operator delta and prove that it satisfies properties similar to the commutative case. In particular when it has associative order 2 the new product is a strictly associative product of degree +1 and there is compatibility between the products, similar to ordinary BV-algebras. We consider several examples of structures obtained in this way. In particular we obtain an A∞-structure on the bar complex of an A∞-algebra that is strictly associative if the original algebra is strictly associative. We also introduce strictly associative degree +1 products for any degree +1 action on a graded algebra. Moreover, an A∞-structure is constructed on the Hochschild cocomplex of an associative algebra with a non-degenerate inner product by using Connes’ B-operator.

Börjeson, Kaj, 1989- (författare)
A Algebras Derived from Associative Algebras with a Non-Derivation Differential
2015
Ingår i: Journal of Generalized Lie Theory and Applications. - : OMICS Publishing Group. - 1736-5279 .- 1736-4337. ; 9:1
Tidskriftsartikel (refereegranskat)abstract
- Given an associative graded algebra equipped with a degree +1 differential delta we define an A∞-structure that measures the failure of delta to be a derivation. This can be seen as a non-commutative analog of generalized BV-algebras. In that spirit we introduce a notion of associative order for the operator delta and prove that it satisfies properties similar to the commutative case. In particular when it has associative order 2 the new product is a strictly associative product of degree +1 and there is compatibility between the products, similar to ordinary BV-algebras. We consider several examples of structures obtained in this way. In particular we obtain an A∞-structure on the bar complex of an A∞-algebra that is strictly associative if the original algebra is strictly associative. We also introduce strictly associative degree +1 products for any degree +1 action on a graded algebra. Moreover, an A∞-structure is constructed on the Hochschild cocomplex of an associative algebra with a non-degenerate inner product by using Connes’ B-operator.

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