scholarly journals Algebraic Group Actions in the Cohomology Theory of Lie Algebras of Cartan Type

1996 ◽  
Vol 179 (3) ◽  
pp. 852-888 ◽  
Author(s):  
Zongzhu Lin ◽  
Daniel K. Nakano
Keyword(s):  
Algebraic Group ◽  
Lie Algebras ◽  
Group Actions ◽  
Cohomology Theory ◽  
Cartan Type

scholarly journals From Lie algebras of vector fields to algebraic group actions

2003 ◽  
Vol 8 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Arjeh M. Cohen ◽  
Jan Draisma
Keyword(s):  
Algebraic Group ◽  
Lie Algebras ◽  
Vector Fields ◽  
Group Actions

scholarly journals Invariants and separating morphisms for algebraic group actions

2015 ◽  
Vol 280 (1-2) ◽  
pp. 231-255 ◽  
Author(s):  
Emilie Dufresne ◽  
Hanspeter Kraft
Keyword(s):  
Algebraic Group ◽  
Group Actions

scholarly journals On the minimal modules for exceptional Lie algebras: Jordan blocks and stabilizers

2016 ◽  
Vol 19 (1) ◽  
pp. 235-258 ◽  
Author(s):  
David I. Stewart
Keyword(s):  
Algebraic Group ◽  
Lie Algebras ◽  
Nilpotent Orbit ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Exceptional Lie Algebras ◽  
Induced Module ◽  
Simply Connected

Let $G$ be a simple simply connected exceptional algebraic group of type $G_{2}$, $F_{4}$, $E_{6}$ or $E_{7}$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mathfrak{g}=\text{Lie}(G)$. For each nilpotent orbit $G\cdot e$ of $\mathfrak{g}$, we list the Jordan blocks of the action of $e$ on the minimal induced module $V_{\text{min}}$ of $\mathfrak{g}$. We also establish when the centralizers $G_{v}$ of vectors $v\in V_{\text{min}}$ and stabilizers $\text{Stab}_{G}\langle v\rangle$ of $1$-spaces $\langle v\rangle \subset V_{\text{min}}$ are smooth; that is, when $\dim G_{v}=\dim \mathfrak{g}_{v}$ or $\dim \text{Stab}_{G}\langle v\rangle =\dim \text{Stab}_{\mathfrak{g}}\langle v\rangle$.

Restricted Envelopes of Lie Superalgebras

2015 ◽  
Vol 22 (02) ◽  
pp. 309-320
Author(s):  
Liping Sun ◽  
Wende Liu ◽  
Xiaocheng Gao ◽  
Boying Wu
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Cartan Type ◽  
Modular Lie Algebras ◽  
Modular Lie Superalgebras

Certain important results concerning p-envelopes of modular Lie algebras are generalized to the super-case. In particular, any p-envelope of the Lie algebra of a Lie superalgebra can be naturally extended to a restricted envelope of the Lie superalgebra. As an application, a theorem on the representations of Lie superalgebras is given, which is a super-version of Iwasawa's theorem in Lie algebra case. As an example, the minimal restricted envelopes are computed for three series of modular Lie superalgebras of Cartan type.

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