On the irreducible module of quantum group Uq(B2) at a root of 1

1994 ◽  
Vol 27 (7) ◽  
pp. 2401-2405
Author(s):  
Shanyou Zhou
Keyword(s):  
Quantum Group ◽  
Irreducible Module

QUANTUM SUPERGROUPS, LINK POLYNOMIALS AND REPRESENTATION OF THE BRAID GENERATOR

1993 ◽  
Vol 05 (02) ◽  
pp. 345-361 ◽  
Author(s):  
J. R. LINKS ◽  
M. D. GOULD ◽  
R. B. ZHANG
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Symmetric Tensor ◽  
Irreducible Module ◽  
Closed Formula ◽  
Cyclic Module ◽  
Tensor Representation ◽  
Finite Dimensional ◽  
Quantum Supergroup ◽  
Rank 2

Unlike the quantum group case, it is shown that the braid generator σ is not always diagonalizable on V ⊗ V, V an irreducible module for a quantum supergroup. Nevertheless a generalization of the Reshetikhin form of the braid generator, obtained previously for quantum groups, is determined corresponding to every finite dimensional standard cyclic module V of a quantum supergroup. This result is applied to obtain a general closed formula for link polynomials arising from standard cyclic modules of a quantum supergroup belonging to a certain class. As explicit examples we determine link polynomials corresponding to the rank 2 symmetric tensor representation of Uq [gl(m|m)] and the defining representation of Uq [osp(2n|2n)].

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

scholarly journals The Real Forms of the Fractional Supergroup SL(2,C)

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 933
Author(s):  
Yasemen Ucan ◽  
Resat Kosker
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
The Real ◽  
And Mathematics ◽  
Real Forms

The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL2,C is one of these important groups. There are real forms of the classical Lie group SL2,C and the quantum group SL2,C in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A3NSL2,C, for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A31SL2,C and A32SL2,C.

Rotational spectra of deformed nuclei and the quantum group SUq (2)

1992 ◽  
Vol 42 (12) ◽  
pp. 1337-1344 ◽  
Author(s):  
M. Honusek ◽  
M. Vinduśka ◽  
V. Wagner
Keyword(s):  
Quantum Group ◽  
Deformed Nuclei ◽  
Rotational Spectra

Jones polynomial invariants for knots and satellites

1991 ◽  
Vol 109 (1) ◽  
pp. 83-103 ◽  
Author(s):  
H. R. Morton ◽  
P. Strickland
Keyword(s):  
Quantum Group ◽  
Linear Combination ◽  
Simple Formula ◽  
Jones Polynomial ◽  
Polynomial Invariants ◽  
Satellite Link ◽  
Representation Ring ◽  
Parallel Links ◽  
Jones Polynomials ◽  
Special Case

AbstractResults of Kirillov and Reshetikhin on constructing invariants of framed links from the quantum group SU(2)q are adapted to give a simple formula relating the invariants for a satellite link to those of the companion and pattern links used in its construction. The special case of parallel links is treated first. It is shown as a consequence that any SU(2)q-invariant of a link L is a linear combination of Jones polynomials of parallels of L, where the combination is determined explicitly from the representation ring of SU(2). As a simple illustration Yamada's relation between the Jones polynomial of the 2-parallel of L and an evaluation of Kauffman's polynomial for sublinks of L is deduced.

Sign in / Sign up

Export Citation Format

Share Document