Results 31 to 40 of about 396,927 (287)
Gelfand-Kirillov dimension of differential difference algebras [PDF]
ACM Communications in Computer Algebra, 2014 AbstractDifferential difference algebras, introduced by Mansfield and Szanto, arose naturally from differential difference equations. In this paper, we investigate the Gelfand–Kirillov dimension of differential difference algebras. We give a lower bound of the Gelfand–Kirillov dimension of a differential difference algebra and a sufficient condition ...
Zhang, Yang, Zhao, Xiangui
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Heisenberg realization for U_q(sln) on the flag manifold [PDF]
, 1993 We give the Heisenberg realization for the quantum algebra $U_q(sl_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(sl_n)$ on the $q$-symmetric algebra $A_q(Mat_n)$ by the Borel-Weil like ...
A. Matsuo +19 more
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(q,t)-deformed (skew) Hurwitz τ-functions
Nuclear Physics B, 2023 We follow the general recipe for constructing commutative families of W-operators, which provides Hurwitz-like expansions in symmetric functions (Macdonald polynomials), in order to obtain a difference operator example that gives rise to a (q,t ...
Fan Liu +6 more
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Ideal Theory and Algebraic Difference Equations [PDF]
Transactions of the American Mathematical Society, 1939 J. F. Rittt introduced the idea of irreducible system of algebraic differential equations and showed that every system of such equations is equivalent to a finite set of irreducible systems. One of the objects of this paper is to develop a special type of abstract ideal theory which has Ritt's theorem as a consequence.
Ritt, J. F., Raudenbush, H. W. jun.
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Matrix factorization for solutions of the Yang-Baxter equation
, 2015 We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra.
Chicherin, D., Derkachov, S.
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Discrete Miura Opers and Solutions of the Bethe Ansatz Equations [PDF]
, 2004 Solutions of the Bethe ansatz equations associated to the XXX model of a simple Lie algebra come in families called the populations. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra. The proof is based on the
Alexander Varchenko +8 more
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Differential-difference system related to toroidal Lie algebra
, 2001 We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky's (2+1)-dimensional KdV hierarchy.
Bogoyavlensky O I +14 more
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Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
, 2017 The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra $o(3,1)$ as its maximal finite-dimensional subalgebra.
Levi, Decio +2 more
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Group algebras and enveloping algebras with nonmatrix and semigroup identities
, 1998 Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity not satisfied
David M. Riley +6 more
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On the algebra of symmetries of Laplace and Dirac operators [PDF]
, 2018 We consider a generalization of the classical Laplace operator, which includes the Laplace-Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators.
De Bie, Hendrik +2 more
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