RESEARCH ARTICLE

Color cyclic homology and Steinberg Lie color algebras

  • Yongjie WANG 1 ,
  • Shikui SHANG 1 ,
  • Yun GAO , 1,2
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  • 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • 2. Department of Mathematics and Statistics, York University, Toronto, Ontario M3J 1P3, Canada

Received date: 07 Mar 2015

Accepted date: 18 Mar 2015

Published date: 24 Jun 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

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 /2-graded version of cyclic homology that was introduced by Kassel) to calculate the universal central extension of Steinberg Lie color algebras.

Cite this article

Yongjie WANG , Shikui SHANG , Yun GAO . Color cyclic homology and Steinberg Lie color algebras[J]. Frontiers of Mathematics in China, 2015 , 10(5) : 1179 -1202 . DOI: 10.1007/s11464-015-0468-9

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