Multiplication alteration by two-cocycles for bialgebras with weak antipode
نویسندگان
چکیده
منابع مشابه
Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproducts
We study how the comultiplication on a Hopf algebra can be modified in such a way that the new comultiplication together with the original multiplication and a suitable antipode gives a new Hopf algebra. To this end, we have to study Harrison type cocycles, and it turns out that there is a relation with the Yang-Baxter equation. The construction is applied to deform the coalgebra structure on t...
متن کاملYetter-drinfeld Modules over Weak Bialgebras
We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. If H is finitely generated and p...
متن کاملLax Bialgebras and Up-To Techniques for Weak Bisimulations
Up-to techniques are useful tools for optimising proofs of behavioural equivalence of processes. Bisimulations up-to context can be safely used in any language specified by GSOS rules. We showed this result in a previous paper by exploiting the well-known observation by Turi and Plotkin that such languages form bialgebras. In this paper, we prove the soundness of up-to contextual closure for we...
متن کاملTwo- and three-cocycles for Laver tables
We determine all 2and 3-cocycles for Laver tables, an infinite sequence of finite structures obeying the left-selfdistributivity law; in particular, we describe simple explicit bases. This provides a number of new positive braid invariants and paves the way for further potential topological applications. An important tool for constructing a combinatorially meaningful basis of 2-cocycles is the ...
متن کاملGraphical Methods for Tannaka Duality of Weak Bialgebras and Weak Hopf Algebras
Tannaka duality describes the relationship between algebraic objects in a given category and functors into that category; an important case is that of Hopf algebras and their categories of representations; these have strong monoidal forgetful “fibre functors” to the category of vector spaces. We simultaneously generalize the theory of Tannaka duality in two ways: first, we replace Hopf algebras...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2019
ISSN: 1303-6149
DOI: 10.3906/mat-1811-55