An interesting group in the operator algebra generated by Hodge's star and the exterior derivative

C.S. Sharma and U. Egele

Physica A: Statistical Mechanics and its Applications, 1982, vol. 114, issue 1, 413-415

Abstract: Hodge's star ∗ and the exterior derivative d generate an algebra A over C, which if regarded as an algebra over its centre is four-dimensional. The centre is the polynomial ring C[k] over C generated by k = d∗ + ∗d. If it is assumed that k is invertible, then the centre is C[k] + C[1k] and it becomes possible to choose a basis for the algebra in such a way that the four elements with their negatives constitute the dihedral group D4 under multiplication. The study of how the group arises provides considerable insight into the structures of both the algebra under consideration and D4.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:114:y:1982:i:1:p:413-415

DOI: 10.1016/0378-4371(82)90322-3

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