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Title: On the third cohomology of algebraic groups of rank two in positive characteristic

We evaluate the third cohomology of simple simply connected algebraic groups of rank 2 over an algebraically closed field of positive characteristic with coefficients in simple modules. It is assumed that the characteristic p of the field is greater than 3 for SL{sub 3}, greater than 5 for Sp{sub 4}, and greater than 11 for G{sub 2}. It follows from the main result that the dimensions of the cohomology spaces do not exceed the rank of the algebraic group in question. To prove the main results we study the properties of the first-quadrant Lyndon-Hochschild-Serre spectral sequence with respect to an infinitesimal subgroup, namely, the Frobenius kernel of the given algebraic group. Bibliography: 49 titles.
Authors:
 [1] ;  [2]
  1. Institute of mathematics Ministry of Education and Science of the Republic of Kazakhstan, Almaty (Kazakhstan)
  2. Bolashak University, Kyzylorda (Kazakhstan)
Publication Date:
OSTI Identifier:
22365578
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 3; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ALGEBRA; GROUP THEORY; KERNELS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; SPACE