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Noncommutative Symmetric Algebras of Two-Sided Vector Spaces

✍ Scribed by David Patrick

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 141 KB
Volume: 233
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8445

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✦ Synopsis

We generalize the definition of the symmetric algebra of a vector space in order to define noncommutative symmetric algebras of two-sided vector spaces. Not all two-sided vector spaces have noncommutative symmetric algebras; the ones that do are called admissible, and conditions for admissibility are given. Further, for some classes of admissible two-sided vector spaces, the skew fields of fractions of their noncommutative symmetric algebras are computed. The degree 0 components of these skew fields correspond to function fields of certain noncommutative ruled surfaces, and hence allow us to determine birational equivalence classes for such surfaces.

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