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http://dx.doi.org/10.4134/BKMS.b200639

A NOTE ON THE FINITE-DIMENSIONAL ODD CONTACT SUPERALGEBRA OVER A FIELD OF PRIME CHARACTERISTIC

Hong, Weidong (School of Mathematics Liaoning University)
Xu, Xiaoning (School of Mathematics Liaoning University)

Publication Information

Bulletin of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1129-1147 More about this Journal

Abstract

This paper aims to analyze the PTG module for the finite-dimensional odd Contact superalgebra over a field of prime characteristic by using the method of Hu and Shen's mixed product realization. The general acting law in odd Contact superalgebra is obtained. In addition, the structure and irreducibility of graded module for odd Contact superalgebra are discussed.

Keywords

Modular Lie superalgebra; weight; irreducible;

Citations & Related Records

Reference

1	R. R. Holmes, Simple restricted modules for the restricted contact Lie algebras, Proc. Amer. Math. Soc. 116 (1992), no. 2, 329-337. https://doi.org/10.2307/2159737 DOI
2	Q. Mu, L. Ren, and Y. Zhang, Ad-nilpotent elements, isomorphisms, and the Weisfeiler filtration of infinite-dimensional modular odd contact superalgebras, Comm. Algebra 39 (2011), no. 10, 3581-3593. https://doi.org/10.1080/00927872.2010.502162 DOI
3	G. Y. Shen, Graded modules of graded Lie algebras of Cartan type. I. Mixed products of modules, Sci. Sinica Ser. A 29 (1986), no. 6, 570-581.
4	G. Y. Shen, Graded modules of graded Lie algebras of Cartan type. III. Irreducible modules, Chinese Ann. Math. Ser. B 9 (1988), no. 4, 404-417.
5	Y. Su and R. B. Zhang, Generalised Verma modules for the orthosympletic Lie superalgebra osp_k\|2, J. Algebra 357 (2012), 94-115. https://doi.org/10.1016/j.jalgebra.2012.01.026 DOI
6	B. Shu and Y.-F. Yao, Character formulas for restricted simple modules of the special superalgebras, Math. Nachr. 285 (2012), no. 8-9, 1107-1116. https://doi.org/10.1002/mana.201000064 DOI
7	H. Strade and R. Farnsteiner, Modular Lie algebras and their representations, Monographs and Textbooks in Pure and Applied Mathematics, 116, Marcel Dekker, Inc., New York, 1988.
8	J. Yuan, W. Liu, and W. Bai, Associative forms and second cohomologies of Lie superalgebras HO and KO, J. Lie Theory 23 (2013), no. 1, 203-215.
9	K. Zheng and Y. Zhang, Some properties of generalized reduced Verma modules over Z-graded modular Lie superalgebras, Czechoslovak Math. J. 67(142) (2017), no. 3, 699-713. https://doi.org/10.21136/CMJ.2017.0050-16 DOI
10	Y. Z. Zhang and W. D. Liu, Modular Lie Superalgebras, Science Press, Beijing, 2004.
11	J. Fu, Q. Zhang, and C. Jiang, The Cartan-type modular Lie superalgebra KO, Comm. Algebra 34 (2006), no. 1, 107-128. https://doi.org/10.1080/00927870500346065 DOI
12	R. Farnsteiner and H. Strade, Shapiro's lemma and its consequences in the cohomology theory of modular Lie algebras, Math. Z. 206 (1991), no. 1, 153-168. https://doi.org/10.1007/BF02571333 DOI
13	N. H. Hu, The graded modules for the graded contact Cartan algebras, Comm. Algebra 22 (1994), no. 11, 4475-4497. https://doi.org/10.1080/00927879408825082 DOI
14	G. Y. Shen, Graded modules of graded Lie algebras of Cartan type. II. Positive and negative graded modules, Sci. Sinica Ser. A 29 (1986), no. 10, 1009-1019.
15	B. Shu and C. Zhang, Representations of the restricted Cartan type Lie superalgebra W(m, n, 1), Algebr. Represent. Theory 14 (2011), no. 3, 463-481. https://doi.org/10.1007/s10468-009-9198-6 DOI
16	Y.-F. Yao and B. Shu, Restricted representations of Lie superalgebras of Hamiltonian type, Algebr. Represent. Theory 16 (2013), no. 3, 615-632. https://doi.org/10.1007/s10468-011-9322-2 DOI
17	Y. Chen and W. Liu, Finite-dimensional odd contact superalgebras over a field of prime characteristic, J. Lie Theory 21 (2011), no. 3, 729-754.
18	R. Farnsteiner, Extension functors of modular Lie algebras, Math. Ann. 288 (1990), no. 4, 713-730. https://doi.org/10.1007/BF01444560 DOI