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Efficient decomposition of separable algebras

โœ Scribed by W. Eberly; M. Giesbrecht

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
657 KB
Volume
37
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

We present new, efficient algorithms for computations on separable matrix algebras over infinite fields. We provide a probabilistic method of the Monte Carlo type to find a generator for the center of a given algebra A โŠ† F mร—m over an infinite field F. The number of operations used is within a logarithmic factor of the cost of solving m ร— m systems of linear equations. A Las Vegas algorithm is also provided under the assumption that a basis and set of generators for the given algebra are available. These new techniques yield a partial factorization of the minimal polynomial of the generator that is computed, which may reduce the cost of computing simple components of the algebra in some cases.

๐Ÿ“œ SIMILAR VOLUMES

Efficient Decomposition of Associative A
Efficient Decomposition of Associative Algebras over Finite Fields
โœ W. Eberly; M. Giesbrecht ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 369 KB

We present new, efficient algorithms for some fundamental computations with finitedimensional (but not necessarily commutative) associative algebras over finite fields. For a semisimple algebra A we show how to compute a complete Wedderburn decomposition of A as a direct sum of simple algebras, an i