On the restricted Lie algebra structure for the Witt Lie algebra in finite characteristic

2001/11/27 by Tyler J. Evans, Evans, Tyler J., Dmitry Fuchs +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.math/0111271

6 Pages

arxiv created 2001/11/27 · openalex publication_date 2001/11/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the p-operator in the Witt algebra (the restricted Lie algebra of derivations of the quotient of the polynomial algebra over a field of characteristic p by the ideal generated by the p-th power of the indeterminant) is given by multiplication by a scalar.

Related

• Quantizations of the Witt algebra and of simple Lie algebras in characteristic p
• Polynomial representations of the Witt Lie algebra
• Simple Lie algebras which generalize Witt algebras
• On structure of graded restricted simple Lie algebras of Cartan type as modules over the Witt algebra
• Restricted Cohomology of Modular Witt Algebras