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- W4300395678 abstract "We show under what conditions the complex computing general Ext-groups carries the structure of a cyclic operad such that Ext becomes a Batalin-Vilkovisky algebra. This is achieved by transferring cyclic cohomology theories for the dual of a (left) Hopf algebroid to the complex in question, which asks for the notion of contramodules introduced along with comodules by Eilenberg-Moore half a century ago. Another crucial ingredient is an explicit formula for the inverse of the Hopf-Galois map on the dual, by which we illustrate recent categorical results and answer a long-standing open question. As an application, we prove that the Hochschild cohomology of an associative algebra A is Batalin-Vilkovisky if A itself is a contramodule over its enveloping algebra A otimes A^op. This is, for example, the case for symmetric algebras and Frobenius algebras with semisimple Nakayama automorphism. We also recover the construction for Hopf algebras." @default.
- W4300395678 created "2022-10-03" @default.
- W4300395678 creator A5075910172 @default.
- W4300395678 date "2016-10-04" @default.
- W4300395678 modified "2023-09-27" @default.
- W4300395678 title "When Ext is a Batalin-Vilkovisky algebra" @default.
- W4300395678 doi "https://doi.org/10.48550/arxiv.1610.01229" @default.
- W4300395678 hasPublicationYear "2016" @default.
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