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On Chevalley Restriction Theorem for Semi-reductive Algebraic Groups and Its Applications

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Ou Ke 1 *   Shu Bin 2   Yao Yufeng 3  
文摘 An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular representations of non-classical finite-dimensional simple Lie algebras in positive characteristic, and some other cases. Let G be a connected semi-reductive algebraic group over an algebraically closed field F and g = Lie(G). It turns out that G has many same properties as reductive groups, such as the Bruhat decomposition. In this note, we obtain an analogue of classical Chevalley restriction theorem for g, which says that the G-invariant ring F[g]~G is a polynomial ring if g satisfies a certain “positivity” condition suited for lots of cases we are interested in. As applications, we further investigate the nilpotent cones and resolutions of singularities for semi-reductive Lie algebras.
来源 Acta Mathematica Sinica. English Series ,2022,38(8):1421-1435 【核心库】
DOI 10.1007/s10114-022-1037-2
关键词 Semi-reductive algebraic groups ; semi-reductive Lie algebras ; Chevalley restriction theorem ; nilpotent cone ; Steinberg map ; Springer resolution
地址

1. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221  

2. School of Mathematical Sciences, East China Normal University, Shanghai, 200241  

3. Department of Mathematics, Shanghai Maritime University, Shanghai, 201306

语种 英文
文献类型 研究性论文
ISSN 1439-8516
学科 数学
基金 国家自然科学基金 ;  Shanghai Key Laboratory of PMMP ;  the Fundamental Research Funds of Yunnan Province
文献收藏号 CSCD:7279300

参考文献 共 28 共2页

1.  Borel A. Linear Algebraic Groups, Second Enlarged Edition. Graduate Texts in Mathematics, Vol. 126,1991 CSCD被引 1 次    
2.  Chevalley C. Invariants of finite groups generated by reflections. Amer. J. Math,1955,77:778-782 CSCD被引 7 次    
3.  Duflo M. Operateurs diffrentiels bi-invariants sur un groupe de Lie. Ann. Sci. Ecole Norm. Sup,1977,10(4):265-288 CSCD被引 2 次    
4.  Humphreys J E. Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, Vol. 9,1972 CSCD被引 6 次    
5.  Humphreys J E. Conjugacy Classes in Semisimple Algebraic Groups,1995 CSCD被引 1 次    
6.  Jantzen J C. Nilpotent Orbits in Representation Theory, Lie Theory, Progr. Math., Vol. 228,2004 CSCD被引 1 次    
7.  Joseph A. Second commutant theorems in enveloping algebraas. Amer. J. Math,1977,99(6):1167-1192 CSCD被引 1 次    
8.  Kostrikin A I. Graded Lie algebras of finite characteristic. Izv. Akad. Nauk SSSR Ser. Mat,1969,33:251-322 CSCD被引 1 次    
9.  Lin Z. Algebraic group actions in the cohomology theory of Lie algebras of Cartan type. J. Algebra,1996,179:852-888 CSCD被引 2 次    
10.  Liu B. Invariants and dualities of a certain parabolic group. arXiv:2111.08281[math.RT] CSCD被引 1 次    
11.  Liu B. Enhanced Brauer algebras and enhanced dualties for orthogonal and symplectic groups. arXiv:2111.08287[math.RT] CSCD被引 1 次    
12.  Luna D. A generalization of the Chevalley restriction theorem. Duke Math. J,1979,46:487-496 CSCD被引 1 次    
13.  Nakano D K. Projective modules over Lie algebras of Cartan type. Mem. Amer. Math. Soc,1992,98(470) CSCD被引 1 次    
14.  Premet A. The theorem on restriction invariants, and nilpotent elements in Wn. Math. USSR Sbornik,1992,73(1):135-159 CSCD被引 1 次    
15.  Premet A. Classification of finite dimensional simple Lie algebras in prime characteristics, Representations of algebraic groups, quantum groups, and Lie algebras. Contemp. Math., Vol. 413,2006:185-214 CSCD被引 1 次    
16.  Ren Y. The BGG category for generalized reductive Lie algebras. arXiv:2010.11849[Math.RT] CSCD被引 1 次    
17.  Strade H. Modular Lie Algebras and Their Representations,1988 CSCD被引 53 次    
18.  Shen G. Graded modules of graded Lie algebras of Cartan type. III. Irreducible modules. Chinese Ann. Math. Ser. B,1988,9(4):404-417 CSCD被引 7 次    
19.  Skryabin S. Independent systems of derivations and Lie algebra representations. Algebra and Analysis (Kazan, 1994),1996:115-150 CSCD被引 2 次    
20.  Springer T. Linear Algebraic Groups, 2nd Edition,1998 CSCD被引 1 次    
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