scholarly journals On universal quadratic identities for minors of quantum matrices

2017 ◽  
Vol 488 ◽  
pp. 145-200
Author(s):  
Vladimir I. Danilov ◽  
Alexander V. Karzanov
Keyword(s):  
Quantum Matrices

scholarly journals AUTOMORPHISMS OF QUANTUM MATRICES

2013 ◽  
Vol 55 (A) ◽  
pp. 89-100 ◽  
Author(s):  
S. LAUNOIS ◽  
T. H. LENAGAN
Keyword(s):  
Automorphism Group ◽  
Quantum Matrices

AbstractWe study the automorphism group of the algebra $\co_q(M_n)$ of n × n generic quantum matrices. We provide evidence for our conjecture that this group is generated by the transposition and the subgroup of those automorphisms acting on the canonical generators of $\co_q(M_n)$ by multiplication by scalars. Moreover, we prove this conjecture in the case when n = 3.

scholarly journals Combinatorics of H-primes in quantum matrices

2007 ◽  
Vol 309 (1) ◽  
pp. 139-167 ◽  
Author(s):  
Stéphane Launois
Keyword(s):  
Quantum Matrices

Quantum matrices in two dimensions

1991 ◽  
Vol 22 (4) ◽  
pp. 297-305 ◽  
Author(s):  
H. Ewen ◽  
O. Ogievetsky ◽  
J. Wess
Keyword(s):  
Two Dimensions ◽  
Quantum Matrices

scholarly journals ORE AND GOLDIE THEOREMS FOR SKEW PBW EXTENSIONS

2013 ◽  
Vol 06 (04) ◽  
pp. 1350061 ◽  
Author(s):  
Oswaldo Lezama ◽  
Juan Pablo Acosta ◽  
Cristian Chaparro ◽  
Ingrid Ojeda ◽  
César Venegas
Keyword(s):  
Commutative Rings ◽  
Polynomial Rings ◽  
Quantum Matrices ◽  
Weyl Algebras ◽  
Skew Polynomial Rings ◽  
Finite Dimensional ◽  
Quantum Version ◽  
Skew Pbw Extensions ◽  
Skew Polynomial ◽  
Finite Dimensional Lie Algebras

Many rings and algebras arising in quantum mechanics can be interpreted as skew Poincaré–Birkhoff–Witt (PBW) extensions. Indeed, Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and its quantization), Artamonov quantum polynomials, diffusion algebras, Manin algebra of quantum matrices, among many others, are examples of skew PBW extensions. In this paper, we extend the classical Ore and Goldie theorems, known for skew polynomial rings, to this wide class of non-commutative rings. As application, we prove the quantum version of the Gelfand–Kirillov conjecture for the skew quantum polynomials.

Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type

1996 ◽  
Vol 119 (1) ◽  
pp. 139-166 ◽  
Author(s):  
Shahn Majid ◽  
Martin Markl
Keyword(s):  
Quantum Groups ◽  
Vector Spaces ◽  
Matrix Group ◽  
Link Invariant ◽  
One Dimensional ◽  
Quantum Matrices ◽  
Link Invariants ◽  
Quantum Vector ◽  
The One ◽  
Quantum Matrix

AbstractWe introduce an associative glueing operation ⊕q on the space of solutions of the Quantum Yang–Baxter Equations of Hecke type. The corresponding glueing operations for the associated quantum groups and quantum vector spaces are also found. The former involves 2×2 quantum matrices whose entries are themselves square or rectangular quantum matrices. The corresponding glueing operation for link-invariants is introduced and involves a state-sum model with Boltzmann weights determined by the link invariants to be glued. The standard su(n) solution, its associated quantum matrix group, quantum space and link-invariant arise at once by repeated glueing of the one-dimensional case.

scholarly journals Cocommutative elements form a maximal commutative subalgebra in quantum matrices

2018 ◽  
Vol 17 (09) ◽  
pp. 1850179
Author(s):  
Szabolcs Mészáros
Keyword(s):  
Trace Formula ◽  
Quantum Matrices ◽  
Root Of Unity ◽  
Commutative Subalgebra ◽  
Maximal Commutative Subalgebra ◽  
Coordinate Rings

In this paper, we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of [Formula: see text], [Formula: see text] and [Formula: see text] are the centralizers of the trace [Formula: see text] in each algebra, for [Formula: see text] being not a root of unity. In particular, it is not only a commutative subalgebra as it was known before, but it is a maximal one.

scholarly journals THE MAXIMAL ORDER PROPERTY FOR QUANTUM DETERMINANTAL RINGS

2003 ◽  
Vol 46 (3) ◽  
pp. 513-529 ◽  
Author(s):  
T. H. Lenagan ◽  
L. Rigal
Keyword(s):  
Maximal Order ◽  
Subject Classification ◽  
Order Property ◽  
Quantum Matrices ◽  
Maximal Orders

AbstractWe develop a method of reducing the size of quantum minors in the algebra of quantum matrices $\mathcal{O}_q(M_n)$. We use the method to show that the quantum determinantal factor rings of $\mathcal{O}_q(M_n)c$ are maximal orders, for $q$ an element of $\mathbb{C}$ transcendental over $\mathbb{Q}$.AMS 2000 Mathematics subject classification: Primary 16P40; 16W35; 20G42

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