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Item Details
| Title:
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ALGEBRA
NONCOMMUTATIVE RINGS IDENTITIES |
| By: |
A. I. Kostrikin (Editor), Yu. A. Bakhturin, Igor Shaferevich |
| Format: |
Hardback |
| List price:
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£72.00 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3540181776 |
| ISBN 13: |
9783540181774 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
1 August, 1991 |
| Series: |
Encyclopaedia of Mathematical Sciences 18 |
| Pages: |
241 |
| Description: |
A survey on the subject of non-commutative rings and algebras, focusing on the theory of identities of these and other algebraic systems. It provides an overview of modern trends encountered in non-commutative algebra. |
| Synopsis: |
The algebra of square matrices of size n ~ 2 over the field of complex numbers is, evidently, the best-known example of a non-commutative alge- 1 bra * Subalgebras and subrings of this algebra (for example, the ring of n x n matrices with integral entries) arise naturally in many areas of mathemat- ics. Historically however, the study of matrix algebras was preceded by the discovery of quatemions which, introduced in 1843 by Hamilton, found ap- plications in the classical mechanics of the past century. Later it turned out that quaternion analysis had important applications in field theory. The al- gebra of quaternions has become one of the classical mathematical objects; it is used, for instance, in algebra, geometry and topology. We will briefly focus on other examples of non-commutative rings and algebras which arise naturally in mathematics and in mathematical physics. The exterior algebra (or Grassmann algebra) is widely used in differential geometry - for example, in geometric theory of integration. Clifford algebras, which include exterior algebras as a special case, have applications in rep- resentation theory and in algebraic topology. The Weyl algebra (Le. algebra of differential operators with* polynomial coefficients) often appears in the representation theory of Lie algebras.In recent years modules over the Weyl algebra and sheaves of such modules became the foundation of the so-called microlocal analysis. The theory of operator algebras (Le. |
| Illustrations: |
biography |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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