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Autor:
Eduard Stiefel, Albert Fässler
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
In conformity with the purpose of this book, we shall here discuss the topics in which group theory methods play a vital part. However, we shall have to confine ourselves to just giving a brief outline of the concepts used in the various fields of ap
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https://doi.org/10.1007/978-1-4612-0395-7_6
https://doi.org/10.1007/978-1-4612-0395-7_6
Autor:
Eduard Stiefel, Albert Fässler
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
The purpose of the present chapter is to give a brief description of some of the notions of crystallography. More detailed treatment of the mathematical theories is available in several texts of the literature (Streitwolf, 1971), (Janssen, 1973), (Br
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https://doi.org/10.1007/978-1-4612-0395-7_8
https://doi.org/10.1007/978-1-4612-0395-7_8
Autor:
Albert Fässler, Eduard Stiefel
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
We resume Example 1.5 where the group G of all proper rotations of the space R3 was introduced. After choosing a cartesian coordinate system (i.e., an orthonormal basis) in R3, we can describe such a rotation by the following matrix A: the kth basis
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https://doi.org/10.1007/978-1-4612-0395-7_4
https://doi.org/10.1007/978-1-4612-0395-7_4
Autor:
Eduard Stiefel, Albert Fässler
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
Even though all considerations made in the subsequent sections are preliminarily meant for finite groups, most statements also extend to a larger class, namely to the class of all compact Lie groups. The latter will not be defined until later in Sect
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https://doi.org/10.1007/978-1-4612-0395-7_5
https://doi.org/10.1007/978-1-4612-0395-7_5
Autor:
Albert Fässler, Eduard Stiefel
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
Externí odkaz:
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https://doi.org/10.1007/978-1-4612-0395-7_7
https://doi.org/10.1007/978-1-4612-0395-7_7
Autor:
Albert Fässler, Eduard Stiefel
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
We now proceed to considerations that are of great importance for the applications. If a problem has a certain symmetry, that is, if it is invariant under a certain set of symmetry operations1, then it cam be considerably simplified and is often solv
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https://doi.org/10.1007/978-1-4612-0395-7_2
https://doi.org/10.1007/978-1-4612-0395-7_2
Autor:
Eduard Stiefel, Albert Fässler
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
The dihedral group D m consists of m rotations and m reflections of the real plane carrying a regular m-sided polygon into itself (see Section 1.9.2).
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https://doi.org/10.1007/978-1-4612-0395-7_3
https://doi.org/10.1007/978-1-4612-0395-7_3
Autor:
Albert Fässler, Eduard Stiefel
Publikováno v:
Group Theoretical Methods and Their Applications ISBN: 9781461267423
Here we discuss the representation theory of the compact Lie groups U(n), SU(n), SO(n)1. We shall describe algorithms to determine the weights of a given representation ϑ in the sense of Cartan’s method (thus generalizing Sections 4.3 and 4.4). Th
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https://doi.org/10.1007/978-1-4612-0395-7_9
https://doi.org/10.1007/978-1-4612-0395-7_9
Publikováno v:
Programmgesteuerte digitale Rechengeräte (elektronische Rechenmaschinen)
Externí odkaz:
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https://doi.org/10.1007/bf02586200
https://doi.org/10.1007/bf02586200
