Lie algebras of linear algebraic groups

Journal of Mathematical Physics, 1973
We study a new class of deformations of algebra representations, namely, i2so(n)⇒sl(n,R), i2u(n)⇒sl(n,C)⊕u(1) and i2sp(n)⊕sp(1)⇒sl(n,Q)⊕sp(1). The new generators are built as commutators between the Casimir invariant of the maximal compact subalgebra and a second-rank mixed tensor.
Boyer, Charles P., Wolf, Kurt Bernardo
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Construction of invariants of the coadjoint representation of Lie groups using linear algebra methods

Theoretical and Mathematical Physics, 2016
After the works of Casimir in 1931, invariant functions of the coadjoint representation were called \textit{Casimir functions}. The study of such invariants is important because of many applications in mathematics and physics. The problem of constructing these representations for semisimple Lie algebras is already solved, although such a problem for ...
Kurnyavko, O. L., Shirokov, I. V.
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Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 2016
We consider a linear differential system [A] : y'=A, y}, where A has with coefficients in C(x). The differential Galois group G of [A] is a linear algebraic group which measures the algebraic relations among solutions. Although there exist general algorithms to compute $G$, none of them is either practical or implemented.
Moulay Barkatou +3 more
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lie algebra
representation theory for linear algebraic groups