Results 1 to 10 of about 42 (40)

Pointed Hopf algebras over nonabelian groups with nonsimple standard braidings

Proceedings of the London Mathematical Society, Volume 127, Issue 4, Page 1185-1245, October 2023., 2023
Abstract We construct finite‐dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We show conversely that every finite‐dimensional pointed Hopf algebra over a nonabelian group with nonsimple ...
Iván Angiono, Simon Lentner, Guillermo Sanmarco   +2 more
wiley   +1 more source

A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras

Bulletin of the London Mathematical Society, Volume 54, Issue 6, Page 2045-2065, December 2022., 2022
Abstract In this paper, we review deformation, cohomology and homotopy theories of relative Rota–Baxter (RB$\mathsf {RB}$) Lie algebras, which have attracted quite much interest recently. Using Voronov's higher derived brackets, one can obtain an L∞$L_\infty$‐algebra whose Maurer–Cartan elements are relative RB$\mathsf {RB}$ Lie algebras.
Yunhe Sheng
wiley   +1 more source

[Retracted] Double Weak Hopf Quiver and Its Path Coalgebra

Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022
The main input of this research is the introduction of the concept of double weak Hopf quiver (DWHQ). In addition, the structures of weak Hopf algebra (WHA) are obtained through path coalgebra of the proposed quivers. Furthermore, the module and comodule structures on the said WHA are discussed.
Muhammad Naseer Khan, Munir Ahmed, Muhammad Arshad, Waleed Almutiry, Rashad A. R. Bantan, Mohammed Elgarhy, Muhammad Gulzar   +6 more
wiley   +1 more source

The Maschke‐Type Theorem and Morita Context for BiHom‐Smash Products

Advances in Mathematical Physics, Volume 2021, Issue 1, 2021., 2021
Let (H, αH, βH, ωH, ψH, SH) be a BiHom‐Hopf algebra and (A, αA, βA) be an (H, αH, βH)‐module BiHom‐algebra. Then, in this paper, we study some properties on the BiHom‐smash product A#H. We construct the Maschke‐type theorem for the BiHom‐smash product A#H and form an associated Morita context AH,AHAA#H,A#HAAH,A#H.
Bingliang Shen, Ling Liu, Yao Zhong Zhang   +2 more
wiley   +1 more source

Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type

Advances in Mathematical Physics, Volume 2021, Issue 1, 2021., 2021
Nichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any Nichols algebras of diagonal type and plays an important role in the classification of Nichols ...
Chen Qian, Jing Wang, Francesco Toppan
wiley   +1 more source

The geometry of the space of branched rough paths

Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 220-251, August 2020., 2020
Abstract We construct an explicit transitive free action of a Banach space of Hölder functions on the space of branched rough paths, which yields in particular a bijection between these two spaces. This endows the space of branched rough paths with the structure of a principal homogeneous space over a Banach space and allows to characterize its ...
Nikolas Tapia, Lorenzo Zambotti
wiley   +1 more source

Quasi‐shuffle algebras and renormalisation of rough differential equations

Bulletin of the London Mathematical Society, Volume 52, Issue 1, Page 43-63, February 2020., 2020
Abstract The objective of this work is to compare several approaches to the process of renormalisation in the context of rough differential equations using the substitution bialgebra on rooted trees known from backward error analysis of B‐series. For this purpose, we present a so‐called arborification of the Hoffman–Ihara theory of quasi‐shuffle ...
Yvain Bruned, Charles Curry, Kurusch Ebrahimi‐Fard   +2 more
wiley   +1 more source

Matching Hom‐Setting of Rota‐Baxter Algebras, Dendriform Algebras, and Pre‐Lie Algebras

Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020
In this paper, we introduce the Hom‐algebra setting of the notions of matching Rota‐Baxter algebras, matching (tri)dendriform algebras, and matching pre‐Lie algebras. Moreover, we study the properties and relationships between categories of these matching Hom‐algebraic structures.
Dan Chen, Xiao-Song Peng, Chia Zargeh, Yi Zhang, Yao-Zhong Zhang   +4 more
wiley   +1 more source

The wonderful compactification for quantum groups

Journal of the London Mathematical Society, Volume 99, Issue 3, Page 778-806, June 2019., 2019
Abstract In this paper, we introduce a quantum version of the wonderful compactification of a group as a certain noncommutative projective scheme. Our approach stems from the fact that the wonderful compactification encodes the asymptotics of matrix coefficients, and from its realization as a GIT quotient of the Vinberg semigroup.
Iordan Ganev
wiley   +1 more source