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Representation theory
In favourable circumstances, every representation is a direct sum of irreducible representations: such representations are said to be semisimple. In this case, it ... More »
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Semisimple Lie algebra - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Semisimple_Lie_algebra
is semisimple, then its center is zero. (Note: since \mathfrak{gl}_n has non-trivial center, it is not semisimple.) In other words, the adjoint representation ...
Semisimple - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Semisimple
In mathematics, the term semisimple (sometimes completely reducible) is used in a number of related ways, within different subjects. The common theme is the ...
www.jstor.org/stable/2001477
TRANSACTIONS OF THE. AMERICAN MATHEMATICAL SOCIETY. Volume 317, Number 2, February. 1990. SEMISIMPLE REPRESENTATIONS OF QUIVERS ...
win.ua.ac.be/~lebruyn/LeBruyn1988b.pdf
the stabilizer subgroup of a semi-simple representation. Since semi-simple representations are precisely those representations V E. R(Q, oz) such that the ...
theory.uchicago.edu/~sethi/Teaching/P385-W2011/texall.p... theory.uchicago.edu/~sethi/Teaching/P385-W2011/texall.pdf
semi-simple Lie algebras, and especially on their representations since it is they, and not just the algebras themselves, which are of greatest interest to the ...
www.math.umass.edu/~jeh/bgg/main.pdf
Representations of Semisimple Lie. Algebras in the BGG Category O. James E. Humphreys. Dept. of Mathematics & Statistics, U. Massachusetts, Amherst, ...
www.math.lsu.edu/~sengupta/notes/finitegrouprepresent.p... www.math.lsu.edu/~sengupta/notes/finitegrouprepresent.pdf
A large part of the route we take passes through the representation theory of semisimple algebras. We will also make a day-tour out of the realm of finite groups ...
www.maths.ed.ac.uk/~ssierra/milicic.pdf
of the current research in representation theory of semisimple Lie groups. In particular, we discuss the theory of “localization” of modules over the envelop- ...
ocw.mit.edu/courses/mathematics/18-712-introduction-to-... ocw.mit.edu/courses/mathematics/18-712-introduction-to-representation-theory-fall-2010/lecture-notes/MIT18_712F10_ch2.pdf
A semisimple (or completely reducible) representation of A is a direct sum of ... with action of A by left multiplication, is a semisimple representation of A, ...
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