scholarly journals JUST NON COMMUTATIVE VARIETIES OF OPERATOR ALGEBRAS AND RINGS WITH SOME CONDITIONS ON NILPOTENT ELEMENTS

1996 ◽  
Vol 27 (1) ◽  
pp. 59-65
Author(s):  
YURI N. MAL'CEV
Keyword(s):  
Operator Algebras ◽  
Finite Ring ◽  
Nilpotent Elements ◽  
Engel Identity

In §1 it is given a classification of Just noncommutative varieties of associative over algebras over commutative Jacobson ring with unity. In [1], [4] are given different proofs of the commutativity of a finite ring with central nilpotent elements. In §2 we give generalizations of these results for infinite rings and for the case of Engel identity.

scholarly journals Construction and classification of holomorphic vertex operator algebras

2020 ◽  
Vol 2020 (759) ◽  
pp. 61-99 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R. Scheithauer
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Vertex Operator Algebras ◽  
Conformal Field Theories ◽  
Cyclic Groups ◽  
Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

scholarly journals Classification of central extensions of Lax operator algebras

2008 ◽  
Author(s):  
Martin Schlichenmaier ◽  
Piotr Kielanowski ◽  
Anatol Odzijewicz ◽  
Martin Schlichenmaier ◽  
Theodore Voronov
Keyword(s):  
Operator Algebras ◽  
Central Extensions ◽  
Lax Operator

Classification of irreducible weak modules over Virasoro vertex operator algebras

2019 ◽  
Vol 30 (11) ◽  
pp. 1950054
Author(s):  
Guobo Chen ◽  
Dejia Cheng ◽  
Jianzhi Han ◽  
Yucai Su
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Positive Integers ◽  
Coprime Positive Integers

The classification of irreducible weak modules over the Virasoro vertex operator algebra [Formula: see text] is obtained in this paper. As one of the main results, we also classify all irreducible weak modules over the simple Virasoro vertex operator algebras [Formula: see text] for [Formula: see text] [Formula: see text], where [Formula: see text] are coprime positive integers.

Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements

2005 ◽  
Vol 3 (3) ◽  
pp. 430-474 ◽  
Author(s):  
Andrzej Daszkiewicz ◽  
Witold Kraśkiewicz ◽  
Tomasz Przebinda
Keyword(s):  
Dual Pairs ◽  
Nilpotent Elements

scholarly journals Classification of extremal vertex operator algebras with two simple modules

2020 ◽  
Vol 61 (5) ◽  
pp. 052302
Author(s):  
J. Connor Grady ◽  
Ching Hung Lam ◽  
James E. Tener ◽  
Hiroshi Yamauchi
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Simple Modules

scholarly journals Rings with a finite set of nonnilpotents

1979 ◽  
Vol 2 (1) ◽  
pp. 121-126 ◽  
Author(s):  
Mohan S. Putcha ◽  
Adil Yaqub
Keyword(s):  
Division Ring ◽  
Nonnegative Integer ◽  
Finite Ring ◽  
Structure Theory ◽  
Nilpotent Elements ◽  
Finite Set ◽  
Semisimple Ring ◽  
Nil Ring ◽  
Primitive Ring

LetRbe a ring and letNdenote the set of nilpotent elements ofR. Letnbe a nonnegative integer. The ringRis called aθn-ring if the number of elements inRwhich are not inNis at mostn. The following theorem is proved: IfRis aθn-ring, thenRis nil orRis finite. Conversely, ifRis a nil ring or a finite ring, thenRis aθn-ring for somen. The proof of this theorem uses the structure theory of rings, beginning with the division ring case, followed by the primitive ring case, and then the semisimple ring case. Finally, the general case is considered.

scholarly journals The classification of modular Lie superalgebras of type M

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Lili Ma ◽  
Liangyun Chen
Keyword(s):  
Intrinsic Property ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Characteristic P ◽  
Infinite Dimensional ◽  
Modular Lie Superalgebra ◽  
Nilpotent Elements ◽  
Natural Filtration ◽  
Modular Lie Superalgebras

AbstractThe natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.

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