### Abstract

Let G be a simple algebraic group over k = C, or F-p where p is good. Set g = Lie G. Given r is an element of N and a faithful (restricted) representation rho: g --> gl(V), one can define a variety of nilpotent elements N-r,(rho)(g) = {x is an element of g: rho(x)(r) = 0}. In this paper we determine this variety when rho is an irreducible representation of minimal dimension or the adjoint representation. (C) 2004 Elsevier Inc. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 719-737 |

Number of pages | 18 |

Journal | Journal of Algebra |

Volume | 280 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 |

### Keywords

- SUPPORT VARIETIES
- UNIPOTENT ELEMENTS
- COHOMOLOGY

## Cite this

Benson, D. J., Boe, B. D., Nakano, D. K., Mazza, N., & UGA VIGRE Algebra Group (2004). Varieties of nilpotent elements for simple Lie algebras I: Good primes.

*Journal of Algebra*,*280*(2), 719-737. https://doi.org/10.1016/j.jalgebra.2004.05.023