The resolution into minimal ideals of the enveloping algebra of the Lie algebra of the rotation group in 4 dimensions with spin 3/2.

Rao, K. N. Srinivasa and Saroja, D. (1966) The resolution into minimal ideals of the enveloping algebra of the Lie algebra of the rotation group in 4 dimensions with spin 3/2. Proceedings of the National Institute of Sciences of India, Part A: Physical Sciences, 32 (3, Cop). pp. 239-50. ISSN 0547-7565

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Abstract

The enveloping algebra of the Lie algebra of the rotation group Rn with half-odd-integral spin is the direct product of the Dirac algebra and another algebra called the ξ-algebra. A complete resoln. into minimal ideals of the ξ-algebra A assocd. with R4 is carried out. The basis of A is shown to be of rank 14, and corresponding to the resoln. 12 + 22 + 32 = 14, three primitive orthogonal idempotent elements of the center of A were detd., thus resolving A into a direct sum of 2-sided ideals Aer (r = 1, 2, 3). Each of these Aer is then resolved into minimal left ideals giving rise to the irreducible representations of A. Since the enveloping algebra L of the Lie algebra of the rotation group in 4 dimension, with the infinitesimal transformations Irs (r � s) satisfying the quartic (Irs2 + 9/4)(Irs2 + 1/4) = 0, is the direct product D � A, the problem of resolving L into minimal left ideals is solved. [on SciFinder(R)]

Item Type: Article
Additional Information: Unmapped bibliographic data: PY - 1966/// [EPrints field already has value set] JA - Proc. Natl. Inst. Sci. India, Part A [Field not mapped to EPrints]
Uncontrolled Keywords: MINIMAL IDEALS RESOLN, RESOLN MINIMAL IDEALS, ROTATION GROUP, ALGEBRAS LIE ENVELOPING, IDEALS MINIMAL RESOLN, LIE ALGEBRAS ENVELOPING, ENVELOPING LIE ALGEBRAS
Subjects: Physical Sciences > Chemistry
Divisions: PG Campuses > Manasagangotri, Mysore > Chemistry
Depositing User: Chandrappa
Date Deposited: 15 May 2013 11:37
Last Modified: 15 May 2013 11:37
URI: http://eprints.uni-mysore.ac.in/id/eprint/8916

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