Singular blocks of restricted sl3

2014/06/04 by Matthew Towers, Towers, Matthew
Mathematics · Physics and Astronomy · #17B35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:17B35

paper · pdf · doi:10.48550/arxiv.1406.1155

openalex publication_date 2014/06/04 · arxiv created 2016/09/23 · arxiv updated 2016/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute generators and relations for the basic algebra of a non-semisimple singular block of the restricted enveloping algebra of \mathfraksl₃ over an algebraically closed field of characteristic p>3. Working directly with the basic algebra we compute its centre and the internal degree zero part of its first Hochschild cohomology, and show its Verma modules are Koszul.

Related

• Explicit calculations in an infinitesimal singular block of SL_N
• The Green ring of a restricted enveloping algebra in characteristic 2
• Cohomology of \fraksl(2) and its applications in prime characteristic
• The Subalgebras of the Real Forms of \(\mathfraksl₃(ℂ)\)
• Koszul duality and Frobenius structure for restricted enveloping algebras