### Abstract

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

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

*Journal of Algebra*,

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

**Varieties of nilpotent elements for simple Lie algebras II: bad primes.** / Benson, David John; Boe, B. D.; Nakano, D. K.; Mazza, Nadia; UGA VIGRE Algebra Group.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Varieties of nilpotent elements for simple Lie algebras II: bad primes

AU - Benson, David John

AU - Boe, B. D.

AU - Nakano, D. K.

AU - Mazza, Nadia

AU - UGA VIGRE Algebra Group

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - SUPPORT VARIETIES

KW - UNIPOTENT

KW - FIELDS

U2 - 10.1016/j.jalgebra.2004.12.023

DO - 10.1016/j.jalgebra.2004.12.023

M3 - Article

VL - 292

SP - 65

EP - 99

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -