Coinvariants for a coadjoint action of quantum matrices

2009 ◽  
Vol 48 (4) ◽  
pp. 239-249 ◽  
Author(s):  
V. V. Antonov ◽  
A. N. Zubkov
Keyword(s):  
Coadjoint Action ◽  
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 On the Structure of Monodromy Algebras and Drinfeld Doubles

1997 ◽  
Vol 09 (03) ◽  
pp. 371-395
Author(s):  
Florian Nill
Keyword(s):  
Hopf Algebra ◽  
Tensor Product ◽  
Tensor Products ◽  
Spin Chains ◽  
Coadjoint Action ◽  
Braided Group ◽  
Gauge Transformations ◽  
Loop Algebras ◽  
Algebraic Tensor Product ◽  
Quasitriangular Hopf Algebra

We give a review and some new relations on the structure of the monodromy algebra (also called loop algebra) associated with a quasitriangular Hopf algebra H. It is shown that as an algebra it coincides with the so-called braided group constructed by S. Majid on the dual of H. Gauge transformations act on monodromy algebras via the coadjoint action. Applying a result of Majid, the resulting crossed product is isomorphic to the Drinfeld double [Formula: see text]. Hence, under the so-called factorizability condition given by N. Reshetikhin and M. Semenov–Tian–Shansky, both algebras are isomorphic to the algebraic tensor product H ⊗ H. It is indicated that in this way the results of Alekseev et al. on lattice current algebras are consistent with the theory of more general Hopf spin chains given by K. Szlachányi and the author. In the Appendix the multi-loop algebras ℒm of Alekseev and Schomerus [3] are identified with braided tensor products of monodromy algebras in the sense of Majid, which leads to an explanation of the "bosonization formula" of [3] representing ℒm as H ⊗…⊗ H.

scholarly journals Combinatorics of H-primes in quantum matrices

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

Characteristic polynomials for quantum matrices

1999 ◽  
pp. 322-329
Author(s):  
A. Isaev ◽  
O. Ogievetsky ◽  
P. Pyatov ◽  
P. Saponov
Keyword(s):  
Characteristic Polynomials ◽  
Quantum Matrices

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

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.

Sign in / Sign up

Export Citation Format

Share Document