Induced representations of lie algebras

Lecture Notes in Mathematics - Topics in Algebra ◽

10.1007/bfb0103130 ◽

1978 ◽

pp. 197-204

Author(s):

William H. Wilson

Keyword(s):

Lie Algebras ◽

Induced Representations ◽

Representations Of Lie Algebras

Induced representations of Lie algebras and a theorem of Borel-Weil.

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1969-0233937-4 ◽

1969 ◽

Vol 136 ◽

pp. 181-181

Author(s):

Nolan R. Wallach

Keyword(s):

Lie Algebras ◽

Induced Representations ◽

Representations Of Lie Algebras

Induced Representations of Lie Algebras and a Theorem of Borel-Weil

Transactions of the American Mathematical Society ◽

10.2307/1994709 ◽

1969 ◽

Vol 136 ◽

pp. 181 ◽

Cited By ~ 1

Author(s):

Nolan R. Wallach

Keyword(s):

Lie Algebras ◽

Induced Representations ◽

Representations Of Lie Algebras

On induced representations of Lie algebras, groups and coalgebras

Journal of Algebra ◽

10.1016/0021-8693(79)90187-x ◽

1979 ◽

Vol 58 (1) ◽

pp. 37-50 ◽

Cited By ~ 1

Author(s):

William H Wilson

Keyword(s):

Lie Algebras ◽

Induced Representations ◽

Representations Of Lie Algebras

Induced representations of Lie algebras. II

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1969-0237590-0 ◽

1969 ◽

Vol 21 (1) ◽

pp. 161-161 ◽

Cited By ~ 9

Author(s):

Nolan R. Wallach

Keyword(s):

Lie Algebras ◽

Induced Representations ◽

Representations Of Lie Algebras

On representations of lie algebras for quantized hamiltonians

Linear Algebra and its Applications ◽

10.1016/s0024-3795(96)00631-3 ◽

1997 ◽

Vol 266 ◽

pp. 69-79 ◽

Cited By ~ 2

Author(s):

L.A-M. Hanna ◽

M.E. Khalifa ◽

S.S. Hassan

Keyword(s):

Lie Algebras ◽

Representations Of Lie Algebras

JOINT SPECTRA OF REPRESENTATIONS OF LIE ALGEBRAS BY COMPACT OPERATORS

Glasgow Mathematical Journal ◽

10.1017/s0017089504001831 ◽

2004 ◽

Vol 46 (2) ◽

pp. 355-362

Author(s):

ENRICO BOASSO

Keyword(s):

Lie Algebras ◽

Compact Operators ◽

Representations Of Lie Algebras

Faithful Representations of Lie Algebras

Collected Papers ◽

10.1007/978-1-4899-7407-5_15 ◽

1984 ◽

pp. 222-230

Author(s):

Harish-Chandra

Keyword(s):

Lie Algebras ◽

Representations Of Lie Algebras

Codimensions of polynomial identities of representations of Lie algebras

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-2013-11622-9 ◽

2013 ◽

Vol 141 (10) ◽

pp. 3369-3382 ◽

Cited By ~ 4

Author(s):

A. S. Gordienko

Keyword(s):

Lie Algebras ◽

Polynomial Identities ◽

Representations Of Lie Algebras

Identities of representations of Lie algebras and *-polynomial identities

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/bf02844386 ◽

1999 ◽

Vol 48 (1) ◽

pp. 153-162 ◽

Cited By ~ 3

Author(s):

Tsetska Rashkova ◽

Vesselin Drensky

Keyword(s):

Lie Algebras ◽

Polynomial Identities ◽

Representations Of Lie Algebras

Representations Subduced on an Ideal of a Lie Algebra

Canadian Journal of Mathematics ◽

10.4153/cjm-1962-021-6 ◽

1962 ◽

Vol 14 ◽

pp. 293-303 ◽

Cited By ~ 1

Author(s):

B. Noonan

Keyword(s):

Irreducible Representation ◽

Lie Algebra ◽

Lie Algebras ◽

Kronecker Product ◽

Point Of View ◽

Irreducible Representations ◽

Closed Field ◽

Algebraically Closed Field ◽

Representations Of Lie Algebras ◽

The Ideal

This paper considers the properties of the representation of a Lie algebra when restricted to an ideal, the subduced* representation of the ideal. This point of view leads to new forms for irreducible representations of Lie algebras, once the concept of matrices of invariance is developed. This concept permits us to show that irreducible representations of a Lie algebra, over an algebraically closed field, can be expressed as a Lie-Kronecker product whose factors are associated with the representation subduced on an ideal. Conversely, if one has such factors, it is shown that they can be put together to give an irreducible representation of the Lie algebra. A valuable guide to this work was supplied by a paper of Clifford (1).