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Decomposition of tensor spaces into irreducible tensor subspaces: An explicit formula of decomposition of the tensor spaces into subspace with trace zero - Couverture souple

Nave, Ophir

 
9783659273667: Decomposition of tensor spaces into irreducible tensor subspaces: An explicit formula of decomposition of the tensor spaces into subspace with trace zero
Couverture souple
ISBN 10 : 365927366X ISBN 13 : 9783659273667
Editeur : LAP LAMBERT Academic Publishing, 2012

Synopsis

The work is organized as follows: We give basic definitions from group theory and group representations, with some examples. We represent all the irreducible representations of the symmetry group S(n), we define the notion of the Young diagram and show that the number of inequivalent irreducible representation of S(n) is the same as the number of different Young diagrams. We also define the Hook formula for dimensions. We give a background of algebraic material and define the Young symmetrizer operator. We give a brief introduction to tensor algebra. In order to clarify the relation between the group GL(V) (in this paper we concentrate on the group S(n)GL(V)) and the tensor space we give an alternative definition of the tensor space T^(n)(V) as C[S(n)]-Module. The standard tableau are defined and the corresponding decomposition of the tensor space is given. We decompose the spaces T^(2)(V); T^(3)(V) and T^(4)(V). We decompose the tensor spaces for n = 2; 3; 4 according to the subgroup O(n) of GL(V). In this work we are dealing with a "bare" vector space. Our main aim is to study the irreducible tensor decompositions of vector spaces with additional structures.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The work is organized as follows: We give basic definitions from group theory and group representations, with some examples. We represent all the irreducible representations of the symmetry group S(n), we define the notion of the Young diagram and show that the number of inequivalent irreducible representation of S(n) is the same as the number of different Young diagrams. We also define the Hook formula for dimensions. We give a background of algebraic material and define the Young symmetrizer operator. We give a brief introduction to tensor algebra. In order to clarify the relation between the group GL(V) (in this paper we concentrate on the group S(n)GL(V)) and the tensor space we give an alternative definition of the tensor space T^(n)(V) as C[S(n)]-Module. The standard tableau are defined and the corresponding decomposition of the tensor space is given. We decompose the spaces T^(2)(V); T^(3)(V) and T^(4)(V). We decompose the tensor spaces for n = 2; 3; 4 according to the subgroup O(n) of GL(V). In this work we are dealing with a "bare" vector space. Our main aim is to study the irreducible tensor decompositions of vector spaces with additional structures.

Biographie de l'auteur

Ophir Nave education: Ph.D. 2010, Applied Mathematics, Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Israel.Advisor: Prof. V. Gol'dshtein.M.Sc. 2005, Mathematics-Physics, Department of mathematics, The Hebrew University of Jerusalem.Advisors: Prof. Shmuel Kaniel and Dr. Ya'akov Itin.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2012
Langue
anglais
ISBN 10 
365927366X
ISBN 13 
9783659273667
Reliure
Broché
Nombre de pages
64
Coordonnées du fabricant
non disponible
Personne responsable
non disponible