Endomorphism Algebras and q-Traces

Details Endomorphism Algebras and q-Traces Endomorphism Algebras and q-Traces

2009-07-01

arxiv.org/abs/0907.0257v3

Journal of Pure and Applied Algebra 214 (2010), pp. 1678-1686

Mathematics

Quantum Algebra

19 pages;typos added; version for the publication of JPAA before proof

Scientific paper

For a braided vector space $(V,\sigma)$ with braiding $\sigma$ of Hecke type, we introduce three associative algebra structures on the space $\oplus_{p=0}^{M}\mathrm{End}S_\sigma^p(V)$ of graded endomorphisms of the quantum symmetric algebra $S_\sigma(V)$. We use the second product to construct a new trace. This trace is an algebra morphism with respect to the third product. In particular, when $V$ is the fundamental representation of $\mathcal{U}_{q}\mathfrak{sl}_{N+1}$ and $\sigma$ is the action of the $R$-matrix, this trace is a scalar multiple of the quantum trace of type $A$.

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