منابع مشابه
Classification of Finite-dimensional Semisimple Lie Algebras
Every finite-dimensional Lie algebra is a semi-direct product of a solvable Lie algebra and a semisimple Lie algebra. Classifying the solvable Lie algebras is difficult, but the semisimple Lie algebras have a relatively easy classification. We discuss in some detail how the representation theory of the particular Lie algebra sl2 tightly controls the structure of general semisimple Lie algebras,...
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We develop a mechanism for classication of isomorphism types of non-trivial semisimple Hopf algebras whose group of grouplikes G(H) is abelian of prime index p which is the smallest prime divisor of |G(H)|. We describe structure of the second cohomology group of extensions of kCp by k G where Cp is a cyclic group of order p and G a finite abelian group. We carry out an explicit classification f...
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A complete set of inequivalent realizations of threeand four-dimensional real unsolvable Lie algebras in vector fields on a space of an arbitrary (finite) number of variables is obtained. Representations of Lie algebras by vector fields are widely applicable e.g. in integrating of ordinary differential equations, group classification of partial differential equations, the theory of differential...
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Computing the structure of a finite-dimensional algebra is a classical mathematical problem in symbolic computation with many applications such as polynomial factorization, computational group theory and differential factorization. We will investigate the computational complexity and exhibit new algorithms for this problem over the field Fq(y), where Fq is the finite field with q elements. A fi...
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We prove tha t each real semisimple Lie algebra g has a Q-form go, such that every real representation of go can be realized over Q. This was previously proved by M. S. Raghunathan (and rediscovered by P. Eberlein) in the special case where g is compact.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.07.016