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Deformations of operator algebras.

Rajczyk, Elias.

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Deformations of operator algebras.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Deformations of operator algebras./
Author:	Rajczyk, Elias.
Description:	73 p.
Notes:	Source: Dissertation Abstracts International, Volume: 57-04, Section: B, page: 2612.
Contained By:	Dissertation Abstracts International57-04B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9625367

Deformations of operator algebras.
Rajczyk, Elias.

Deformations of operator algebras. - 73 p.

Source: Dissertation Abstracts International, Volume: 57-04, Section: B, page: 2612.

Thesis (Ph.D.)--Universitaire Instelling Antwerpen (Belgium), 1996.

The complex numbers, the Subjects--Topical Terms:

515831
Mathematics.

Deformations of operator algebras.
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035 $a (UnM)AAI9625367
035 $a AAI9625367
040 $a UnM $c UnM
100 1 $a Rajczyk, Elias. $3 1903876
245 1 0 $a Deformations of operator algebras.
300 $a 73 p.
500 $a Source: Dissertation Abstracts International, Volume: 57-04, Section: B, page: 2612.
500 $a Adviser: F. Van Oystaeyen.
502 $a Thesis (Ph.D.)--Universitaire Instelling Antwerpen (Belgium), 1996.
520 $a The complex numbers, the $n $ by $n $ matrices, the bounded operators on a Hilbert space are all examples of mathematical structure $a \cdot b $, the so-called algebras.
520 $a I developed a formula which associates to an analytical algebra--all above examples are analytical algebras--a new multiplicative law $a \cdot\sb{t}b $, $t $ is an arbitrary real number.
520 $a The new multiplicative law depends on $t $ and on a set of pre-chosen derivations on the analytical algebra.
520 $a The multiplication $a \cdot\sb{t}b $ may be described through a Taylor series at $t =0 $, the 0-th order term in this series is $a \cdot b $. This allows to consider $a \cdot\sb{t}b $ as a deformation of $a \cdot b $.
520 $a The procedure we just described becomes particularly interesting when it is applied to certain infinite dimensional analytical algebras, like for instance, the continuous functions on the unit circle. The multiplicative structure of the latter is abelian, but the deformed product is not. Through results like this I found that if the deformation is applied on algebras which are basic in classic mechanics, the resulting malgebras are standard objects in quantum mechanics.
520 $a The mathematical study of the multiplication $a \cdot\sb{t}b $ is the central subject of my thesis. I investigate which properties are invariant after performing the deformation and I study the representation theory and mathematical-physical properties of $a \cdot\sb{t}b $.
590 $a School code: 0314.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, General. $3 1018488
690 $a 0405
690 $a 0605
710 2 0 $a Universitaire Instelling Antwerpen (Belgium). $3 1249793
773 0 $t Dissertation Abstracts International $g 57-04B.
790 1 0 $a Oystaeyen, F. Van, $e advisor
790 $a 0314
791 $a Ph.D.
792 $a 1996
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9625367