## Reductive embeddings are Cohen-Macaulay

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**131**(2003), 675-684 Request permission

## Abstract:

In this paper we prove that in positive characteristics normal embeddings of connected reductive groups are Frobenius split. As a consequence, they have rational singularities and are thus Cohen–Macaulay varieties. As an application, we study the particular case of reductive monoids, which are affine embeddings of their unit group. In particular, we show that the algebra of regular functions of a normal irreducible reductive monoid $M$ has a good filtration for the action of the unit group of $M$ .## References

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## Additional Information

**Alvaro Rittatore**- Affiliation: Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay
- Email: alvaro@cmat.edu.uy
- Received by editor(s): September 28, 2000
- Published electronically: October 23, 2002
- Additional Notes: This research was partially done during a stay at the Institut Fourier, Grenoble, France.
- Communicated by: Dan M. Barbasch
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**131**(2003), 675-684 - MSC (2000): Primary 14M17, 14M05
- DOI: https://doi.org/10.1090/S0002-9939-02-06843-0
- MathSciNet review: 1937404