
Algebra II
Noncommutative Rings Identities
Springer (Publisher)
Published on 23. November 2011
Book
Paperback/Softback
VII, 234 pages
978-3-642-72901-0 (ISBN)
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1991
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VII, 234 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 14 mm
Weight
382 gr
ISBN-13
978-3-642-72901-0 (9783642729010)
DOI
10.1007/978-3-642-72899-0
Schweitzer Classification
Other editions
Additional editions
Book
08/1991
Springer
€85.55
Article exhausted; check different version
Content
I. Noncommutative Rings.- II. Identities.- Author Index.