scholarly journals Noncommutative topology and Jordan operator algebras

2018 ◽  
Vol 292 (3) ◽  
pp. 481-510 ◽  
Author(s):  
David P. Blecher ◽  
Matthew Neal
2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Dan Xie ◽  
Wenbin Yan

Abstract We identify vertex operator algebras (VOAs) of a class of Argyres-Douglas (AD) matters with two types of non-abelian flavor symmetries. They are the W algebras defined using nilpotent orbit with partition [qm, 1s]. Gauging above AD matters, we can find VOAs for more general $$ \mathcal{N} $$ N = 2 SCFTs engineered from 6d (2, 0) theories. For example, the VOA for general (AN − 1, Ak − 1) theory is found as the coset of a collection of above W algebras. Various new interesting properties of 2d VOAs such as level-rank duality, conformal embedding, collapsing levels, coset constructions for known VOAs can be derived from 4d theory.


Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.


2021 ◽  
Vol 573 ◽  
pp. 451-475
Author(s):  
Hiromichi Yamada ◽  
Hiroshi Yamauchi

2020 ◽  
Vol 18 (1) ◽  
pp. 1615-1624
Author(s):  
Guangyu An ◽  
Ying Yao

Abstract In this paper, we study the Hyers-Ulam-Rassias stability of ( m , n ) (m,n) -Jordan derivations. As applications, we characterize ( m , n ) (m,n) -Jordan derivations on C ⁎ {C}^{\ast } -algebras and some non-self-adjoint operator algebras.


K-Theory ◽  
1991 ◽  
Vol 4 (3) ◽  
pp. 245-267 ◽  
Author(s):  
Klaus Thomsen
Keyword(s):  

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Thomas Creutzig ◽  
Yasuaki Hikida

Abstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described by the $$ \mathfrak{sl}(2)/\mathfrak{u}(1) $$ sl 2 / u 1 coset and sine-Liouville theory. In a previous work, a proof of the FZZ-duality was provided by applying the reduction method from $$ \mathfrak{sl}(2) $$ sl 2 Wess-Zumino-Novikov-Witten model to Liouville field theory and the self-duality of Liouville field theory. In this paper, we work with the coset model of the type $$ \mathfrak{sl}\left(N+1\right)/\left(\mathfrak{sl}(N)\times \mathfrak{u}(1)\right) $$ sl N + 1 / sl N × u 1 and investigate the equivalence to a theory with an $$ \mathfrak{sl}\left(N+\left.1\right|N\right) $$ sl N + 1 N structure. We derive the duality explicitly for N = 2, 3 by applying recent works on the reduction method extended for $$ \mathfrak{sl}(N) $$ sl N and the self-duality of Toda field theory. Our results can be regarded as a conformal field theoretic derivation of the duality of the Gaiotto-Rapčák corner vertex operator algebras Y0,N,N+1[ψ] and YN,0,N+1[ψ−1].


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