The Net Advance of Physics:

GROUP THEORY AND ALGEBRA

GROUPS: General and Various + Homotopy + Quantum + Symplectic + Unitary

Abstract Algebra:

GENERAL AND VARIOUS:

• Catalogue of Algebraic Systems, edited by John Pedersen
• Abstract Algebra II, by John A. Beachy Free online graduate-level textbook.

DIVISION ALGEBRAS (CLIFFORD ALGEBRAS, QUATERNIONS):

• Division Algebra FAQ, by David Rusin, 95/02
• Geometric Algebra and its Application to Mathematical Physics, by Chris Doran, (Ph. D. thesis), 1994
• Division Algebras, Sphere Algebras and Twistors, by Martin Cederwall, 93/10
• Introduction to Geometric Algebra, by Stephen Gull, A. N. Lasenby, and Chris Doran, 93/02
• International Clifford Algebra Society Homepage
• CLICAL and Hypercomplex Numbers Homepage, by Pertti Lounesto Includes the hypercomplex algebra computer program CLICAL.
• Letters concerning the Invention of Quaternions, by Sir Wm. R. Hamilton
• The Theory of Extension (excerpts), by Hermann Grassmann Translated by Desmond Fearnley-Sander
• NET ADVANCE OF PHYSICS:Spin and Spinors

GRASSMANN ALGEBRA:

• The Theory of Extension (excerpts), by Hermann Grassmann Translated by Desmond Fearnley-Sander
• Hermann Grassmann and the Creation of Linear Algebra, by Desmond Fearnley-Sander, 1979

HOPF ALGEBRAS:

• Introduction to Yangian in Physics, by Mo-lin Ge, Kang Xue,and Yiwen Wang, 95/09
• Noncommutative Geometry of Finite Groups, by K. Bresser et al., 95/09

LIE ALGEBRAS:

• Angular Momentum Algebra:
  • NET AVANCE OF PHYSICS: Spin
• Quantum:
  • NET ADVANCE OF PHYSICS: Quantum Groups
• Virasoro Algebras:
  • Irrational Conformal Field Theory, by M. B. Halpern et al., 95/01

LINEAR ALGEBRA AND MATRICES:

• General and Various:
  • Linear Algebra Homepage, by David Rusin
• Random Matrices:
  • Random Matrices, by Craig A. Tracy and Harold Widom, 92/10

NONLINEAR ALGEBRAS:

• W-Algebras:
  • Conformal Linearization Versus Nonlinearity of W-Algebras, by S. Krivonos and A. Sorin, 95/10

YANGIAN SYMMETRY:

• Introduction to Yangian in Physics, by Mo-lin Ge, Kang Xue,and Yiwen Wang, 95/09
• An Introduction to Yangian Symmetries, by D. Bernard, 92/11

Fields and Rings:

• GENERAL AND VARIOUS:
  • Rings, by John A. Beachy, 1995 (Postscript file)
  • Notes on Ring Theory, by David Rusin

Group Theory:

GENERAL AND VARIOUS:

• Group Theory (Chapter 3 of "Two Dimensional QCD is a String Theory", thesis by Soeren Koester), 94/08 page 33.

HOMOTOPY GROUPS:

• Order Parameters, Broken Symmetry, and Topology, by James Sethna

QUANTUM GROUPS AND NON-COMMUTATIVE MANIFOLDS:

• General:
  • Supersymmetric Quantum Theory, Non-Commutative Geometry, and Gravitation, by J. Froehlich, et al., 97/06:
  • Simple Field Theoretical Models on Non-Commutative Manifolds, by H. Grosse et al., 95/10
  • Quantum Spaces, by S. L. Woronowicz, R. J. Budzynski, and W. Kondracki, 94/10
  • Non-Commutative Differential Geometry on Quantum Groups, by P. Aschieri and L. Castellani, 92/07
  • Quantized Lie groups and algebras, by T.Tjin, 91/11
  • NET ADVANCE OF PHYSICS: Hopf Algebras
• Type: Braided
  • Braided Geometry and q-Minkowski Space, by Shahn Majid, 94/10
• In Physics:
  • Supersymmetric Quantum Theory, Non-Commutative Geometry, and Gravitation, by J. Froehlich, et al., 97/06:
  • Quantum Algebraic Symmetries in Nuclear Structure, by D. Bonatsos et al., 95/10
  • Non-Commutative Geometric Methods Applied to Particle Physics, by A. H. Chamseddine, 94/10
  • The Liouville Approach to 2D Gravity and its Toda Generalizations, by Jean-Loup Gervais, 92/12
• And Yangian Symmetry:
  • Introduction to Yangian in Physics, by Mo-lin Ge, Kang Xue,and Yiwen Wang, 95/09

SYMPLECTIC GROUPS:

• The Real Symplectic Groups in Quantum Mechanics and Optics, by Arvind et al., 95/09

UNITARY GROUPS:

• SU(2):
  • NET ADVANCE OF PHYSICS:Spin and Spinors
• SU(3):
  • SU3 Isoscalar Factors, by H. Thomas Williams, 95/09

To contribute to this page, write Norman Redington, redingtn@mit.edu

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