Finite irreducible modules of Lie conformal algebras 𝒲(a,b) and some Schrödinger–Virasoro type Lie conformal algebras

2019 ◽  
Vol 30 (06) ◽  
pp. 1950026 ◽  
Author(s):  
Lipeng Luo ◽  
Yanyong Hong ◽  
Zhixiang Wu
Keyword(s):  
Complete Classification ◽  
Conformal Algebra ◽  
Direct Sums ◽  
Conformal Algebras ◽  
Irreducible Modules ◽  
Rank One ◽  
Virasoro Type

Lie conformal algebras [Formula: see text] are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we first give a complete classification of all finite nontrivial irreducible conformal modules of [Formula: see text]. It is shown that all such modules are of rank one. Moreover, with a similar method, all finite nontrivial irreducible conformal modules of Schrödinger–Virasoro type Lie conformal algebras [Formula: see text] and [Formula: see text] are characterized.

scholarly journals Finite irreducible conformal modules of rank two Lie conformal algebras

2020 ◽  
pp. 2150145
Author(s):  
Maosen Xu ◽  
Yanyong Hong ◽  
Zhixiang Wu
Keyword(s):  
Irreducible Module ◽  
Conformal Algebra ◽  
Conformal Algebras ◽  
Irreducible Modules ◽  
Rank One

In the present paper, we prove that any finite nontrivial irreducible module over a rank two Lie conformal algebra [Formula: see text] is of rank one. We also describe the actions of [Formula: see text] on its finite irreducible modules explicitly. Moreover, we show that all finite nontrivial irreducible modules of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie conformal algebra are of rank one.

Finite irreducible representations of map Lie conformal algebras

2017 ◽  
Vol 28 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Henan Wu
Keyword(s):  
Representation Theory ◽  
Associative Algebra ◽  
Complete Classification ◽  
Conformal Algebra ◽  
Irreducible Representations ◽  
Finite Representation ◽  
Finite Dimensional ◽  
Conformal Algebras ◽  
Commutative Associative Algebra

In this paper, we study the finite representation theory of the map Lie conformal algebra [Formula: see text], where G is a finite simple Lie conformal algebra and A is a commutative associative algebra with unity over [Formula: see text]. In particular, we give a complete classification of nontrivial finite irreducible conformal modules of [Formula: see text] provided A is finite-dimensional.

scholarly journals Loop Schrödinger–Virasoro Lie conformal algebra

2016 ◽  
Vol 27 (06) ◽  
pp. 1650057 ◽  
Author(s):  
Haibo Chen ◽  
Jianzhi Han ◽  
Yucai Su ◽  
Ying Xu
Keyword(s):  
Lie Algebra ◽  
Conformal Algebra ◽  
Cohomology Groups ◽  
Conformal Algebras ◽  
Rank One ◽  
Intermediate Series

In this paper, we introduce two kinds of Lie conformal algebras, associated with the loop Schrödinger–Virasoro Lie algebra and the extended loop Schrödinger–Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and [Formula: see text]-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.

scholarly journals Inductive limit of direct sums of simple TAI algebras

2019 ◽  
pp. 1-26
Author(s):  
Bo Cui ◽  
Chunlan Jiang ◽  
Liangqing Li
Keyword(s):  
Inductive Limit ◽  
Direct Sums ◽  
Rank Zero ◽  
C Algebra ◽  
C Algebras ◽  
Rank One ◽  
Tracial Rank ◽  
Ideal Property ◽  
Funct Anal

An ATAI (or ATAF, respectively) algebra, introduced in [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404] (or in [X. C. Fang, The classification of certain non-simple C*-algebras of tracial rank zero, J. Funct. Anal. 256 (2009) 3861–3891], respectively) is an inductive limit [Formula: see text], where each [Formula: see text] is a simple separable nuclear TAI (or TAF) C*-algebra with UCT property. In [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404], the second author classified all ATAI algebras by an invariant consisting orderd total [Formula: see text]-theory and tracial state spaces of cut down algebras under an extra restriction that all element in [Formula: see text] are torsion. In this paper, we remove this restriction, and obtained the classification for all ATAI algebras with the Hausdorffized algebraic [Formula: see text]-group as an addition to the invariant used in [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404]. The theorem is proved by reducing the class to the classification theorem of [Formula: see text] algebras with ideal property which is done in [G. Gong, C. Jiang and L. Li, A classification of inductive limit C*-algebras with ideal property, preprint (2016), arXiv:1607.07681]. Our theorem generalizes the main theorem of [X. C. Fang, The classification of certain non-simple C*-algebras of tracial rank zero, J. Funct. Anal. 256 (2009) 3861–3891], [C. Jiang, A classification of non simple C*-algebras of tracial rank one: Inductive limit of finite direct sums of simple TAI C*-algebras, J. Topol. Anal. 3 (2011) 385–404] (see Corollary 4.3).

scholarly journals Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra

10.1063/1.4979619 ◽  
2017 ◽  
Vol 58 (4) ◽  
pp. 041701 ◽  
Author(s):  
Henan Wu ◽  
Lamei Yuan
Keyword(s):  
Conformal Algebra ◽  
Conformal Algebras

Extensions of finite irreducible modules of Lie conformal algebras W(a,b) and some Schrödinger-Virasoro type Lie conformal algebras

2020 ◽  
Vol 48 (11) ◽  
pp. 4774-4795
Author(s):  
Lipeng Luo ◽  
Yanyong Hong ◽  
Zhixiang Wu
Keyword(s):  
Conformal Algebras ◽  
Irreducible Modules ◽  
Virasoro Type

Lie conformal algebras related to Galilean conformal algebras

2020 ◽  
pp. 2150075
Author(s):  
Xiu Han ◽  
Dengyin Wang ◽  
Chunguang Xia
Keyword(s):  
Conformal Algebra ◽  
Complex Numbers ◽  
Conformal Algebras ◽  
Rank One ◽  
Intermediate Series

Let [Formula: see text] be a Lie conformal algebra related to Galilean conformal algebras, where [Formula: see text] are complex numbers. All the conformal derivations of [Formula: see text] are shown to be inner. The rank one conformal modules and [Formula: see text]-graded free intermediate series modules over [Formula: see text] are completely classified. The corresponding results of the finite conformal subalgebra of [Formula: see text] are also obtained as byproducts.

scholarly journals On the classification of 5d SCFTs

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Lakshya Bhardwaj
Keyword(s):  
Complete Classification ◽  
Geometric Description ◽  
Rank One ◽  
Computationally Intensive ◽  
First Time

Abstract We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5d KK theories.

A CLASSIFICATION OF NON-SIMPLE C*-ALGEBRAS OF TRACIAL RANK ONE: INDUCTIVE LIMITS OF FINITE DIRECT SUMS OF SIMPLE TAI C*-ALGEBRAS

2011 ◽  
Vol 03 (03) ◽  
pp. 385-404 ◽  
Author(s):  
CHUNLAN JIANG
Keyword(s):  
Compatibility Conditions ◽  
Inductive Limits ◽  
Direct Sums ◽  
State Spaces ◽  
Tracial State ◽  
C Algebras ◽  
Rank One ◽  
Tracial Rank ◽  
Unital Simple

In this paper, we will classify the class of C*-algebras which are inductive limits of finite direct sums of unital simple separable nuclear C*-algebras with tracial rank no more than one (or equivalently TAI algebras) with torsion K1-group which satisfy the UCT. The invariant consists of ordered total K-theory and the tracial state spaces of cutdown algebras (with certain compatibility conditions).

A class of Schrödinger–Virasoro type Lie conformal algebras

2015 ◽  
Vol 26 (08) ◽  
pp. 1550058 ◽  
Author(s):  
Wei Wang ◽  
Ying Xu ◽  
Chunguang Xia
Keyword(s):  
Lie Algebra ◽  
Cohomology Group ◽  
Conformal Algebra ◽  
Conformal Algebras ◽  
Virasoro Type

In this paper, a class of Lie conformal algebras associated to a Schrödinger–Virasoro type Lie algebra is constructed, which is nonsimple and can be regarded as an extension of the Virasoro conformal algebra. Then conformal derivations, second cohomology group with trivial coefficients and conformal modules of rank 1 of this Lie conformal algebra are investigated.

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