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The Universal Askey-Wilson Algebra and DAHA of Type (C_1^∨,C_1)
Symmetry, Integrability and Geometry: Methods and Applications, 2013 Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $Delta_q$ of AW(3) called the universal Askey-Wilson algebra.
Paul Terwilliger
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The Algebraic Sets of Broad Algebras
Известия Иркутского государственного университета: Серия "Математика", 2020 The paper is devoted to the questions of algebraic geometry of universal algebras, more precisely, to the structures of algebraic sets of this algebras. It is introduced the concept of broad universal algebra.
A.G. Pinus
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Pseudo-free families of computational universal algebras
Journal of Mathematical Cryptology, 2020 Let Ω be a finite set of finitary operation symbols. We initiate the study of (weakly) pseudo-free families of computational Ω-algebras in arbitrary varieties of Ω-algebras.
Anokhin Mikhail
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Homogeneous Structures: Model Theory meets Universal Algebra (online meeting) [PDF]
, 2021 The workshop "Homogeneous Structures: Model Theory meets Universal Algebra'' was centred around transferring recently obtained advances in universal algebra from the finite to the infinite.
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De Morgan algebras are universal
Discrete Mathematics, 1987 A concrete category K is called universal if the category of graphs and compatible mappings can be fully embedded into K. A bounded distributive lattice L with a unary operation \(\sim\) satisfying the identities \(\sim (a\wedge b)=\sim a\vee \sim b\), \(\sim (a\vee b)=\sim a\wedge \sim b\), \(\sim \sim a=a\) is called a de Morgan algebra.
Adams, M, Priestley, H
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Quantum groups, Yang–Baxter maps and quasi-determinants
Nuclear Physics B, 2018 For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang–Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum ...
Zengo Tsuboi
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Congruences and subdirect representations of graphs
Electronic Journal of Graph Theory and Applications, 2020 A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined for graphs with properties similar to their universal algebraic counterparts.
Stefan Veldsman
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Structure coefficients of the Hecke algebra of $(\mathcal{S}_{2n}, \mathcal{B}_n)$ [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The Hecke algebra of the pair $(\mathcal{S}_{2n}, \mathcal{B}_n)$, where $\mathcal{B}_n$ is the hyperoctahedral subgroup of $\mathcal{S}_{2n}$, was introduced by James in 1961. It is a natural analogue of the center of the symmetric group algebra.
Omar Tout
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Universal Framework for Quantum Error-Correcting Codes
Entropy, 2021 We present a universal framework for quantum error-correcting codes, i.e., a framework that applies to the most general quantum error-correcting codes. This framework is based on the group algebra, an algebraic notation associated with nice error bases ...
Zhuo Li, Lijuan Xing
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