General Cartan, Borel and Parabolic Subalgebras of $$\mathfrak {gl} (\infty )$$ and $$\mathfrak {sl}(\infty )$$

Springer Monographs in Mathematics - Classical Lie Algebras at Infinity ◽

10.1007/978-3-030-89660-7_6 ◽

2021 ◽

pp. 69-85

Author(s):

Ivan Penkov ◽

Crystal Hoyt

Keyword(s):

Parabolic Subalgebras

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Levi components of parabolic subalgebras of finitary Lie algebras

Representation Theory and Mathematical Physics - Contemporary Mathematics ◽

10.1090/conm/557/11029 ◽

2011 ◽

pp. 129-149 ◽

Author(s):

Elizabeth Dan-Cohen ◽

Ivan Penkov

Keyword(s):

Lie Algebras ◽

Parabolic Subalgebras

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Nonlinear maps satisfying derivability on standard parabolic subalgebras of finite-dimensional simple Lie algebras

Linear and Multilinear Algebra ◽

10.1080/03081080903402921 ◽

2011 ◽

Vol 59 (3) ◽

pp. 261-270 ◽

Author(s):

Zhengxin Chen ◽

Dengyin Wang

Keyword(s):

Lie Algebras ◽

Simple Lie Algebras ◽

Finite Dimensional ◽

Parabolic Subalgebras ◽

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Biderivations and strong commutativity-preserving maps on parabolic subalgebras of simple Lie algebras

Linear and Multilinear Algebra ◽

10.1080/03081087.2020.1809621 ◽

2020 ◽

pp. 1-13

Author(s):

Zhengxin Chen ◽

Yalong Yu

Keyword(s):

Lie Algebras ◽

Simple Lie Algebras ◽

Parabolic Subalgebras ◽

Strong Commutativity Preserving ◽

Strong Commutativity

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On commuting varieties of parabolic subalgebras

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2017.04.015 ◽

2018 ◽

Vol 222 (3) ◽

pp. 491-507 ◽

Author(s):

Russell Goddard ◽

Simon M. Goodwin

Keyword(s):

Parabolic Subalgebras

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On the Classical Double of Parabolic Subalgebras

Communications in Algebra ◽

10.1081/agb-200027721 ◽

2004 ◽

Vol 32 (10) ◽

pp. 3787-3796

Author(s):

Iulia Pop

Keyword(s):

Parabolic Subalgebras

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Braided Enveloping Algebras Associated to Quantum Parabolic Subalgebras

Communications in Algebra ◽

10.1080/00927872.2010.498394 ◽

2011 ◽

Vol 39 (10) ◽

pp. 3491-3514 ◽

Author(s):

Jan E. Grabowski

Keyword(s):

Enveloping Algebras ◽

Parabolic Subalgebras

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On Reducibility Criterions for Scalar Generalized Verma Modules Associated to Maximal Parabolic Subalgebras

Springer Proceedings in Mathematics & Statistics - Lie Theory and Its Applications in Physics ◽

10.1007/978-981-10-2636-2_34 ◽

2016 ◽

pp. 465-473 ◽

Author(s):

Toshihisa Kubo

Keyword(s):

Verma Modules ◽

Parabolic Subalgebras ◽

Generalized Verma Modules

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Nonlinear maps satisfying derivability on the parabolic subalgebras of the general linear Lie algebras

Linear and Multilinear Algebra ◽

10.1080/03081087.2011.574627 ◽

2012 ◽

Vol 60 (2) ◽

pp. 149-157 ◽

Author(s):

Zhengxin Chen ◽

Dengyin Wang

Keyword(s):

Lie Algebras ◽

General Linear ◽

Parabolic Subalgebras ◽

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Parabolic subalgebras and gradings of reductive Lie superalgebras

Journal of Mathematical Sciences ◽

10.1007/s10958-008-9049-8 ◽

2008 ◽

Vol 152 (1) ◽

pp. 1-60 ◽

Author(s):

N. I. Ivanova ◽

A. L. Onishchik

Keyword(s):

Lie Superalgebras ◽

Parabolic Subalgebras

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On the homomorphisms between scalar generalized Verma modules

Compositio Mathematica ◽

10.1112/s0010437x13007677 ◽

2014 ◽

Vol 150 (5) ◽

pp. 877-892 ◽

Author(s):

Hisayosi Matumoto

Keyword(s):

Verma Modules ◽

Parabolic Subalgebras ◽

Generalized Verma Modules

AbstractIn this article, we study the homomorphisms between scalar generalized Verma modules. We conjecture that any homomorphism between scalar generalized Verma modules is a composition of elementary homomorphisms. The purpose of this article is to confirm the conjecture for some parabolic subalgebras under the assumption that the infinitesimal characters are regular.

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