Course Details
Subject {L-T-P / C} : MA6645 : Group Theory and its Application { 3-1-0 / 4}
Subject Nature : Theory
Coordinator : Dr. Bikramaditya Sahu
Syllabus
General and special linear groups, bilinear forms, Symplectic groups, symmetric forms, quadratic forms, Orthogonal geometry, orthogonal groups, Clifford algebras, Hermitian forms, Unitary spaces, Unitary groups.
Course Objectives
- To give an introduction to different types of finite classical groups
- To study the simplicity of Sympletic, Orthogonal and Unitary groups
- To study some applications in Finite Geometry
Course Outcomes
This course will help students to learn certain matrix groups over finite fields and their simplicity. This will help to do research in finite geometry, representation theory and related areas.
Essential Reading
- L. C. Grove, Classical Groups and Geometric Algebra, Graduate Studies in Mathematics 39, American Mathematical Society, 2002
- E. Artin, Geometric Algebra, John Wiley & sons, 1988
Supplementary Reading
- L. M. Batten, Combinatorics of Finite Geometries, Cambridge University Press, 1997
- G. E. Moorhouse, Incidence Geometry, 2007, available online from http://www.uwyo.edu/moorhouse/handouts/incidence geometry.pdf