Algebra II: Noncommutative Rings Identities - Couverture souple

Couverture souple

ISBN 10 : 3642729010 ISBN 13 : 9783642729010

Editeur : Springer, 2011

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2011
• ISBN 10: 3642729010
• ISBN 13: 9783642729010
• Reliure: Broché
• Langue: anglais
• Nombre de pages: 248
• Éditeur: Kostrikin A.I., Shafarevich I.R.
• Coordonnées du fabricant: non disponible