Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896425 | Journal of Algebra | 2018 | 11 Pages |
Abstract
We study p-Brauer characters of a finite group G which are restrictions of generalized characters vanishing on p-singular elements for a fixed prime p dividing the order of G. Such Brauer characters are called quasi-projective. We show that for each irreducible Brauer character Ï there exists a minimal p-power, say pa(Ï), such that pa(Ï)Ï is quasi-projective. The exponent a(Ï) only depends on the Cartan matrix of the block to which Ï belongs. Moreover pa(Ï) is bounded by the vertex of the module affording Ï, and equality holds in case that G is p-solvable. We give some evidence for the conjecture that a(Ï)=0 occurs if and only if Ï belongs to a block of defect 0. Finally, we study indecomposable quasi-projective Brauer characters of a block B. This set is finite and corresponds to a minimal Hilbert basis of the rational cone defined by the Cartan matrix of B.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yanjun Liu, Wolfgang Willems,