Gröbner–Shirshov Bases for Universal Enveloping Conformal Algebras of Simple Conformal Lie Superalgebras of Type WN

2004 ◽  
Vol 43 (2) ◽  
pp. 109-122 ◽  
Author(s):  
P. S. Kolesnikov
Keyword(s):  
Lie Superalgebras ◽  
Conformal Algebras

CLASSICAL LIE SUPERALGEBRAS OVER SIMPLE ASSOCIATIVE ALGEBRAS

2006 ◽  
Vol 92 (3) ◽  
pp. 581-600 ◽  
Author(s):  
GEORGIA BENKART ◽  
XIAOPING XU ◽  
KAIMING ZHAO
Keyword(s):  
Lie Algebras ◽  
Associative Algebra ◽  
Weyl Algebra ◽  
Identity Element ◽  
Lie Superalgebras ◽  
Associative Algebras ◽  
Matrix Algebras ◽  
Weyl Algebras ◽  
Conformal Algebras ◽  
The Matrix

Over arbitrary fields of characteristic not equal to 2, we construct three families of simple Lie algebras and six families of simple Lie superalgebras of matrices with entries chosen from different one-sided ideals of a simple associative algebra. These families correspond to the classical Lie algebras and superalgebras. Our constructions intermix the structure of the associative algebra and the structure of the matrix algebra in an essential, compatible way. Many examples of simple associative algebras without an identity element arise as a by-product. The study of conformal algebras and superalgebras often involves matrix algebras over associative algebras such as Weyl algebras, and for that reason, we illustrate our constructions by taking various one-sided ideals from a Weyl algebra or a quantum torus.

scholarly journals Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1381-1391
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Arbitrary Field ◽  
Special Linear ◽  
Highest Weight ◽  
Irreducible Modules

Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.

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