Color cyclic homology and Steinberg Lie color algebras

Abstract

The present paper contains two interrelated developments. First, the basic properties of the construction theory over the Steinberg Lie color algebras are developed in analogy with Steinberg Lie algebra case. This is done on the example of the central closed of the Steinberg Lie color algebras. The second development is that we define the first ϵ-cyclic homology group HC₁(R, ϵ) of the Γ-graded associative algebra R (which could be seemed as the generalization of cyclic homology group and the \mathbb{Z}/\mathrm{2}\mathbb{Z}-graded version of cyclic homology that was introduced by Kassel) to calculate the universal central extension of Steinberg Lie color algebras.

Keywords

Steinberg Lie color algebra / ϵ-cyclic homology group / universal central extension

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