Results 21 to 30 of about 52 (51)
[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 +6 more
wiley +1 more source
Quantization of the Super‐BMS3 Algebra
Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022 In this article, we study quantization of super‐BMS3 algebra W. We quantize W by the Drinfel’d twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras.
Yu Yang, Xing Tao Wang, Francesco Toppan
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 +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
Physical constraints on quantum deformations of spacetime symmetries
Nuclear Physics B, 2018 In this work we study the deformations into Lie bialgebras of the three relativistic Lie algebras: de Sitter, Anti-de Sitter and Poincaré, which describe the symmetries of the three maximally symmetric spacetimes. These algebras represent the centerpiece
Flavio Mercati, Matteo Sergola
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The κ-(A)dS quantum algebra in (3+1) dimensions
Physics Letters B, 2017 The quantum duality principle is used to obtain explicitly the Poisson analogue of the κ-(A)dS quantum algebra in (3+1) dimensions as the corresponding Poisson–Lie structure on the dual solvable Lie group.
Ángel Ballesteros +3 more
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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
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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 +2 more
wiley +1 more source
On the Cohomology and Extensions of n‐ary Multiplicative Hom‐Nambu‐Lie Superalgebras
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 In this paper, we discuss the representations of n‐ary multiplicative Hom‐Nambu‐Lie superalgebras as a generalization of the notion of representations for n‐ary multiplicative Hom‐Nambu‐Lie algebras. We also give the cohomology of an n‐ary multiplicative Hom‐Nambu‐Lie superalgebra and obtain a relation between extensions of an n‐ary multiplicative Hom ...
Lijun Tian +3 more
wiley +1 more source
Quantization of the Rank Two Heisenberg–Virasoro Algebra
AxiomsQuantum groups occupy a significant position in both mathematics and physics, contributing to progress in these fields. It is interesting to obtain new quantum groups by the quantization of Lie bialgebras.
Xue Chen
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