The GL-module structure of the Hochschild homology of truncated tensor algebras

AMES, GUILLERMO; CAGLIERO, LEANDRO; TIRAO, PAULO

JOURNAL OF PURE AND APPLIED ALGEBRA

ELSEVIER SCIENCE BV

Año: 2004 vol. 193 p. 11 - 26

0022-4049

Let $A$ be the tensor algebra of a complex vector space $V$, divided by a power of the augmentation ideal. The authors of this paper study the decomposition of the Hochschild homology $HH(A)$ of $A$, under the natural action of ${ m GL}(V)$. This uses a specific resolution of $A$ as a bimodule due to M. J. Bardzell ef[J. Algebra 188 (1997), no. 1, 69--89; MR1432347 (98a:16009)], as well as results of representation theory, such as the Schur duality, Young diagrams, and formulae involving characters. Apart from results of general flavor, potentially useful explicit computations are given, in particular cases.