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From Bar construction to quantum groups, and back to (co)homology via braidings.

Prof. Marc Rosso
Sunday, November 25th, 2018, 8:00 AM  闵行数学楼401报告厅
报告人简介:Rosso是著名Hopf代数与量子群专家。他博士毕业于Stasbourg大学,现为巴黎七大教授。他是法国巴黎高等师范学校数学系前任系主任,Bourbaki学派成员。他的文章发表在顶尖杂志Invent. Math.等国际杂志上,具有巨大的学术影响力。

Abstract: The Bar construction for an associative algebra involves the classical cofree coalgebra, with a suitable coderivation. Extending the context to the category of Hopf bimodules over a Hopf algebra, one gets a cofree coalgebra whose universal property provides a product (quantum shuffle) involving braidings. Specific examples lead to a simple construction of quantum groups. Quantized (co)shuffles also lead to complexes on tensor powers of braided vector spaces. Given an algebra A, there is a natural map s on its tensor square such that (A, s) being a braided vector space is equivalent to associativity of A. Then the associated complex is exactly the Hochschild complex. (The last part is work of V. Lebed).

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