scholarly journals Characters of infinite-dimensional quantum classical groups: BCD cases

2021 ◽  
Author(s):  
Ryosuke Sato
Keyword(s):  
Representation Theory ◽  
Character Theory ◽  
Compact Groups ◽  
Markov Semigroups ◽  
Inductive Limits ◽  
Universal Enveloping Algebras ◽  
Infinite Dimensional ◽  
Enveloping Algebras ◽  
Quantized Universal Enveloping Algebras ◽  
The Relationship

We study the character theory of inductive limits of [Formula: see text]-deformed classical compact groups. In particular, we clarify the relationship between the representation theory of Drinfeld–Jimbo quantized universal enveloping algebras and our previous work on the quantized characters. We also apply the character theory to construct Markov semigroups on unitary duals of [Formula: see text], [Formula: see text], and their inductive limits.

scholarly journals Character theory of infinite wreath products

2005 ◽  
Vol 2005 (9) ◽  
pp. 1365-1379 ◽  
Author(s):  
Robert Boyer
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Finite Groups ◽  
Wreath Products ◽  
Character Theory ◽  
Group Algebras ◽  
Inductive Limits ◽  
Infinite Symmetric Group ◽  
The Relationship ◽  
Asymptotic Character

The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” TheK0-invariant of the groupC∗-algebra is also determined.

scholarly journals Recursion formulas for HOMFLY and Kauffman invariants

2014 ◽  
Vol 23 (05) ◽  
pp. 1450024
Author(s):  
Qingtao Chen ◽  
Nicolai Reshetikhin
Keyword(s):  
Universal Enveloping Algebras ◽  
Recursion Relations ◽  
Enveloping Algebras ◽  
Recursion Formulas ◽  
Quantized Universal Enveloping Algebras ◽  
Two Parameter

In this paper, we describe the recursion relations between two parameter HOMFLY and Kauffman polynomials of framed links. These relations correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings gn ⊃ gk × sln-k where gn is either so2n+1, so2n or sp2n is new.

scholarly journals On the Relationship between Jordan Algebras and Their Universal Enveloping Algebras

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
F. B. H. Jamjoom ◽  
A. H. Al Otaibi
Keyword(s):  
State Space ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
The State ◽  
Jordan Algebras ◽  
Universal Enveloping Algebras ◽  
Von Neumann ◽  
Enveloping Algebras ◽  
Normal States ◽  
The Relationship

The relationship between JW-algebras (resp. JC-algebras) and their universal enveloping von Neumann algebras (resp. C ∗ -algebras) can be described as significant and influential. Examples of numerous relationships have been established. In this article, we established a relationship between the set of split faces of the state space (resp. normal states) of a JC-algebra (resp. a JW-algebra) and the set of split faces of the state space (resp. normal states) of its universal enveloping C ∗ -algebra (resp. von Neumann algebra), and we tied up this relationship with the correspondence between the classes of invariant faces, closed ideals, and central projections of these Jordan algebras and of their universal enveloping algebras.

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