Results 21 to 30 of about 3,096 (57)
The Elliptic GL(n) Dynamical Quantum Group as an đ„âHopf Algebroid
International Journal of Mathematics and Mathematical Sciences, Volume 2009, Issue 1, 2009., 2009 Using the language of đ„âHopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, â±ell(GL(n)), from the elliptic solution of the quantum dynamical YangâBaxter equation with spectral parameter associated to the Lie algebra đ°đ©n. We apply the generalized FRST construction and obtain an đ„âbialgebroid â±ell(M(n)).
Jonas T. Hartwig, Francois Goichot
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Homologies of Algebraic Structures via Braidings and Quantum Shuffles [PDF]
, 2012 In this paper we construct "structural" pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some of these pre-braidings seem original.
Lebed, Victoria
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Asymmetric graphs with quantum symmetry
Proceedings of the London Mathematical Society, Volume 131, Issue 5, November 2025.Abstract We present an infinite sequence of finite graphs with trivial automorphism group and nonâtrivial quantum automorphism group. These are the first known examples of graphs with this property. Moreover, to the best of our knowledge, these are the first examples of any asymmetric classical space that has nonâtrivial quantum symmetries.
Josse van Dobben de Bruyn +2 more
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A Comparison of Deformations and Geometric Study of Varieties of Associative Algebras
International Journal of Mathematics and Mathematical Sciences, Volume 2007, Issue 1, 2007., 2007 The aim of this paper is to give an overview and to compare the different deformation theories of algebraic structures. In each case we describe the corresponding notions of degeneration and rigidity. We illustrate these notions by examples and give some general properties.
Abdenacer Makhlouf, Howard E. Bell
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Quantum continuous $gl_\infty$: Tensor products of Fock modules and $W_n$ characters
, 2010 We construct a family of irreducible representations of the quantum continuous $gl_\infty$ whose characters coincide with the characters of representations in the minimal models of the $W_n$ algebras of $gl_n$ type.
Feigin, B. +4 more
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Modular representations of the Yangian Y2$Y_2$
Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.Abstract Let Y2$Y_2$ be the Yangian associated to the general linear Lie algebra gl2$\mathfrak {gl}_2$, defined over an algebraically closed field k$\mathbb {k}$ of characteristic p>0$p>0$. In this paper, we study the representation theory of the restricted Yangian Y2[p]$Y^{[p]}_2$.
Hao Chang, Jinxin Hu, Lewis Topley
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The dynamical U(n) quantum group
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We study the dynamical analogue of the matrix algebra M(n), constructed from a dynamical Râmatrix given by Etingof and Varchenko. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these ...
Erik Koelink, Yvette Van Norden
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Four dimensional topological quantum field theory, Hopf categories, and the canonical bases
, 1994 We propose a new mwthod of constructing 4D-TQFTs. The method uses a new type of algebraic structure called a Hopf Category. We also outline the construction of a family of Hopf categories related to the quantum groups, using the canonical bases.Comment ...
Beilinson A. +4 more
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Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract We construct a family of solvable lattice models whose partition functions include p$p$âadic Whittaker functions for general linear groups from two very different sources: from Iwahoriâfixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, we uncover unexpected relationships between Iwahori and metaplectic ...
Ben Brubaker +3 more
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On linear difference equations over rings and modules
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 5, Page 239-258, 2004., 2004 We develop a coalgebraic approach to the study of solutions of linear difference equations over modules and rings. Some known results about linearly recursive sequences over base fields are generalized to linearly (bi)recursive (bi)sequences of modules over arbitrary commutative ground rings.
Jawad Y. Abuhlail
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