On the cyclic Deligne conjecture

By Thomas Tradler, M. Zeinalian. 2004

65 citations recorded by the source corpus.

Abstract Let A be a finite dimensional, unital, and associative algebra which is endowed with a non-degenerate and invariant inner product. We give an explicit description of an action of cyclic Sullivan chord diagrams on the normalized Hochschild cochain complex of A . As a corollary, the Hochschild cohomology of A becomes a Frobenius algebra which is endowed with a compatible BV operator. If A is also commutative, then the discussion extends to an action of general Sullivan chord diagrams. Some implications of this are discussed.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bee044f41c3db1d21e63e60147289faf781506ca

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In Mathematical Physics

Citations in the corpus

Moduli space actions on the Hochschild co-chains of a Frobenius algebra I: cell operads (2006, methodology): “There are many definitions of Sullivan chord diagrams in the literature [CS, S1, S2, CG, TZ ].”
Topological conformal field theories and Calabi–Yau categories (2004, background): “nn surfaces on the Hochschild chains. The original Deligne’s conjecture has been proved by Tamarkin [23], Kontsevich and Soibelman [11], McClure and Smith [14], Kaufmann [5, 6], Tradler and Zeinalian [24]. A diﬀerent approach to constructing an action of chains on higher genus moduli spaces on Hochs”
Hochschild homology of structured algebras (2011, unknown): “The equivalence relation in [57] corresponds this way to the one defined here.”