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Mac Lane Method for Determination of Extensions of Finite Groups. II. An Example for the Dihedral Group D_{2}

100%

Lulek T., Chatterjee R.

Acta Physica Polonica A

1992

vol. 82

issue 3

395-406

The Mac Lane method of classification and construction of all extensions of a group Q by an Abelian group T is demonstrated on the case Q = D_{2}, T = C_{2}. Constructions involving free groups and operator homomorphisms are performed in detail, and the complete list of resulting extensions is given. It is shown that there are 8 classes of gauge equivalency, and they fall into 4 classes of isomorphism. The role of gauge transformations is pointed out. Physical contexts of various constructions are reviewed. A comparison with the direct cohomology definitions is performed.

Electronic Spaces and Classification of Multielectron States in Multicentre Systems

81%

Chatterjee R., Lulek T., Biel J.

Acta Physica Polonica A

1992

vol. 81

issue 4-5

467-474

Electronic structure of a crystal within the tight binding model is described in terms of fibre bundle formalism, with the base and fiber being respectively the set of all sites and the single-centre space of electron spinorbitals. It is based on the Weyl's duality between the symmetric group and the unitary group, and paves the way for a Racah-Wigner type of description of electronic structure in multicentre systems.

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2 Acta Physica Polonica A

2 1992

2 Chatterjee R.

2 Lulek T.

1 Biel J.

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Mac Lane Method for Determination of Extensions of Finite Groups. II. An Example for the Dihedral Group D_{2}

Electronic Spaces and Classification of Multielectron States in Multicentre Systems