Restricted Kac modules for special contact Lie superalgebras of odd type

2020 ◽  
Vol 15 (2) ◽  
pp. 419-434
Author(s):  
Shujuan Wang ◽  
Jixia Yuan ◽  
Wende Liu
Keyword(s):  
Lie Superalgebras ◽  
Kac Modules

scholarly journals Complexity for modules over the classical Lie superalgebra

2012 ◽  
Vol 148 (5) ◽  
pp. 1561-1592 ◽  
Author(s):  
Brian D. Boe ◽  
Jonathan R. Kujawa ◽  
Daniel K. Nakano
Keyword(s):  
Lie Algebra ◽  
Lie Superalgebra ◽  
Projective Resolution ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Minimal Projective Resolution ◽  
Finite Dimensional ◽  
Reductive Lie Algebra ◽  
Completely Reducible ◽  
Kac Modules

AbstractLet ${\Xmathfrak g}={\Xmathfrak g}_{\zerox }\oplus {\Xmathfrak g}_{\onex }$ be a classical Lie superalgebra and let ℱ be the category of finite-dimensional ${\Xmathfrak g}$-supermodules which are completely reducible over the reductive Lie algebra ${\Xmathfrak g}_{\zerox }$. In [B. D. Boe, J. R. Kujawa and D. K. Nakano, Complexity and module varieties for classical Lie superalgebras, Int. Math. Res. Not. IMRN (2011), 696–724], we demonstrated that for any module M in ℱ the rate of growth of the minimal projective resolution (i.e. the complexity of M) is bounded by the dimension of ${\Xmathfrak g}_{\onex }$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\Xmathfrak {gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.

scholarly journals Primitive vectors of Kac-modules of the Lie superalgebras sl(m/n)

2000 ◽  
Vol 41 (7) ◽  
pp. 5064-5087 ◽  
Author(s):  
Yucai Su ◽  
J. W. B. Hughes ◽  
R. C. King
Keyword(s):  
Lie Superalgebras ◽  
Kac Modules

On restricted representations of restricted contact Lie superalgebras of odd type

2016 ◽  
Vol 15 (04) ◽  
pp. 1650075 ◽  
Author(s):  
Shujuan Wang ◽  
Wende Liu
Keyword(s):  
Lie Superalgebras ◽  
Necessary Condition ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Kac Modules ◽  
Sufficient And Necessary Condition

Simple restricted modules are considered for the restricted contact Lie superalgebras of odd type over an algebraically closed field with characteristic [Formula: see text]. In particular, a sufficient and necessary condition in terms of typical or atypical weights is given for the restricted Kac modules to be simple. Furthermore, the number of the simple restricted Kac modules is obtained.

On the composition factors of Kac modules for the Lie superalgebras sl(m/n)

1992 ◽  
Vol 33 (2) ◽  
pp. 470-491 ◽  
Author(s):  
J. W. B. Hughes ◽  
R. C. King ◽  
J. Van der Jeugt
Keyword(s):  
Lie Superalgebras ◽  
Kac Modules ◽  
Composition Factors

scholarly journals Restricted Kac modules of Hamiltonian Lie superalgebras of odd type

2014 ◽  
Vol 178 (3) ◽  
pp. 473-488 ◽  
Author(s):  
Jixia Yuan ◽  
Wende Liu
Keyword(s):  
Lie Superalgebras ◽  
Kac Modules

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.

Sign in / Sign up

Export Citation Format

Share Document