Representations of Lie algebras in prime characteristic

1998 ◽  
pp. 185-235 ◽  
Author(s):  
Jens Carsten Jantzen
Keyword(s):  
Lie Algebras ◽  
Prime Characteristic ◽  
Representations Of Lie Algebras

scholarly journals The Representations of Lie Algebras of Prime Characteristic

1954 ◽  
Vol 2 (1) ◽  
pp. 1-36 ◽  
Author(s):  
Hans Zassenhaus
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Characteristic Zero ◽  
Finite Dimension ◽  
Quotient Ring ◽  
Irreducible Representations ◽  
Indecomposable Representation ◽  
Prime Characteristic ◽  
Representations Of Lie Algebras ◽  
Algebra Over A Field

There are some simple facts which distinguish Lie-algebras over fields of prime characteristic from Lie-algebras over fields of characteristic zero. These are(1) The degrees of the absolutely irreducible representations of a Lie-algebra of prime characteristic are bounded whereas, according to a theorem of H. Weyl, the degrees of the absolutely irreducible representations of a semi-simple Lie-algebra over a field of characteristic zero can be arbitrarily high.(2) For each Lie-algebra of prime characteristic there are indecomposable representations which are not irreducible, whereas every indecomposable representation of a semi-simple Liealgebra over a field of characteristic zero is irreducible (cf. [4]).(3) The quotient ring of the embedding algebra of a Lie-algebra over a field of prime characteristic is a division algebra of finite dimension over its center, whereas this is not the case for characteristic zero. (cf. [4]).(4) There are faithful fully reducible representations of every Lie-algebra of prime characteristic, whereas for characteristic zero only ring sums of semi-simple Lie-algebras and abelian Lie-algebras admit faithful fully reducible representations (cf. [6], [2], [4]).

scholarly journals On representations of lie algebras for quantized hamiltonians

1997 ◽  
Vol 266 ◽  
pp. 69-79 ◽  
Author(s):  
L.A-M. Hanna ◽  
M.E. Khalifa ◽  
S.S. Hassan
Keyword(s):  
Lie Algebras ◽  
Representations Of Lie Algebras

scholarly journals DERIVATIONS OF THE ODD CONTACT LIE ALGEBRAS IN PRIME CHARACTERISTIC

2013 ◽  
Vol 50 (3) ◽  
pp. 591-605
Author(s):  
Yan Cao ◽  
Xiumei Sun ◽  
Jixia Yuan
Keyword(s):  
Lie Algebras ◽  
Prime Characteristic

Representations Subduced on an Ideal of a Lie Algebra

1962 ◽  
Vol 14 ◽  
pp. 293-303 ◽  
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).

scholarly journals Non-singular derivations of solvable Lie algebras in prime characteristic

2020 ◽  
Vol 586 ◽  
pp. 170-189
Author(s):  
Marcos Goulart Lima ◽  
Csaba Schneider
Keyword(s):  
Lie Algebras ◽  
Prime Characteristic ◽  
Solvable Lie Algebras
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