### Abstract

Let G be a simple algebraic group over an algebraically closed field k of characteristic p> 0 and let g be the (restricted) Lie algebra of G with pth power map
[p]. The maximal ideal spectrum of the cohomology ring of the restricted enveloping algebra Maxspec(H2•(u(g), k)) can be identified with the variety N1(g)={x∈g:x[p]=0}. When the characteristic of the field is a good prime, this variety was first described as the closure of a certain Richardson orbit by Carlson, Lin, Nakano and Parshall [4]. Their methods used the techniques developed by Nakano, Parshall and Vella [23] which involved the verification of a conjecture of Jantzen on the support varieties of Weyl modules.

Original language | English |
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Pages (from-to) | 65-99 |

Number of pages | 34 |

Journal | Journal of Algebra |

Volume | 292 |

DOIs | |

Publication status | Published - 2005 |

### Keywords

- SUPPORT VARIETIES
- UNIPOTENT
- FIELDS

## Cite this

Benson, D. J., Boe, B. D., Nakano, D. K., Mazza, N., & UGA VIGRE Algebra Group (2005). Varieties of nilpotent elements for simple Lie algebras II: bad primes.

*Journal of Algebra*,*292*, 65-99. https://doi.org/10.1016/j.jalgebra.2004.12.023