| Algebra II: Noncommutative Rings Identities Softcover Repri Edition Contributor(s): Kostrikin, A. I. (Editor), Shafarevich, I. R. (Editor) |
|
 |
ISBN: 3642729010 ISBN-13: 9783642729010 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Mathematics | Algebra - Abstract |
| Dewey: 512.2 |
| Series: Encyclopaedia of Mathematical Sciences |
| Physical Information: 0.52" H x 6.14" W x 9.21" (0.78 lbs) 234 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |