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

## 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 Î¾-algebra. A complete resoln. into minimal ideals of the Î¾-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 â� s) satisfying the quartic (Irs2 + 9/4)(Irs2 + 1/4) = 0, is the direct product D Ã� A, the problem of resolving L into minimal left ideals is solved. [on SciFinder(R)]

Item Type: | Article |
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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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