# IRREDUCIBLE MODULES OVER THE E6-TYPE LIE ALGEBRA

Kim, Yang-Gon

• Published : 2007.06.25
• 32 2

#### Abstract

Let L := L(G) denote the classical modular Lie algebra of $E_6$-type over an algebraically closed field F of characteristic p > 5 associated with some simple and simply connected algebraic group G. After the prototypes of those for $E_8$-type in [4], we shall search for irreducible (=simple) L-modules in this paper.

#### Keywords

exceptional type;modular representation

#### References

1. C. Curtis, Representations of Lie algebras of classical type with applica­tions to linear groups, J. Math, and Mech. , 9 (1960), 307-326.
2. V.G.Kac, Infinite dimensional Lie algebras, 3rd edition, Cambridge, 1990.
3. Y. G. Kim, Irreducible modules over the $E_7$-type Lie algebra, Korean An­nals of Mathematics , Vol.21, No 2 (2004), 193-198.
4. Y.G.Kim, S-theory (I), Kyung-Moon Publishers, 2001.
5. A.Premet, Support varieties of nonrestricted modules over Lie algebras of reductive groups, Journal of the London Mathematical Society Vol.55, part 2 (1997), 236-250. https://doi.org/10.1112/S0024610797004900
6. H.Strade and R.Farnsteiner, Modular Lie algebras and their representa­tions, Marcel Dekker, 1988.
7. H.Zassenhaus, The representations of Lie algebras of prime characteristic, Proceedings of Glasgow Math Assoc ,No.2, (1954), 1-36.