Noncommutative rings identities
著者
書誌事項
Noncommutative rings identities
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 18 . Algebra ; 2）
Springer-Verlag, c1991
- : gw
- : us
- :pbk
- タイトル別名
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Algebra II
Algebra 2
Fundamental'nye napravlenii︠a︡
Algebra two
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注記
Translation of: Algebra 2, issued as v. 18 of the serial: Itogi nauki i tekhniki. Serii︠a︡ sovremennye problemy matematiki. Fundamental'nye napravlenii︠a︡
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
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: gw ISBN 9783540181774
内容説明
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.
目次
I. Noncommutative Rings.- II. Identities.- Author Index.
- 巻冊次
-
:pbk ISBN 9783642729010
内容説明
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.
目次
I. Noncommutative Rings.- II. Identities.- Author Index.
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