Algebra II by Ai Kostrikin

Algebra II by Ai Kostrikin

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.

SKU	Unavailable
ISBN 13	9783642729010
ISBN 10	3642729010
Title	Algebra II
Author	Ai Kostrikin
Series	Encyclopaedia Of Mathematical Sciences
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2011-11-23
Number of pages	234
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.