11,812 research outputs found
Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras
In this paper generalized Matsumoto-Tits sections lifting permutations to the
algebra associated to a generalized virtual braid monoid are defined. They are
then applied to study the defining relations of the quantum quasi-shuffle
algebras via the total symmetrization operator.Comment: 18 page
On defining ideals and differential algebras of Nichols algebras
This paper is devoted to understanding the defining ideal of a Nichols
algebra from the decomposition of specific elements in the group algebra of
braid groups. A family of primitive elements are found and algorithms are
proposed. To prove the main result, the differential algebra of a Nichols
algebra is constructed. Moreover, another point of view on Serre relations is
provided.Comment: 34 pages, including a list of notation
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