A01=Daniel E. Flath
A01=J. Scott Carter
A01=Masahico Saito
Addition
Allegory (category theory)
Author_Daniel E. Flath
Author_J. Scott Carter
Author_Masahico Saito
Automorphism
Big O notation
Bilinear form
Binomial coefficient
Braid group
Cartesian product
Catalan number
Category=PBW
Category=PHQ
Cobordism
Coefficient
Commutative ring
Computation
Diagram
Diagram (category theory)
Dimension
Dimension (vector space)
Dual space
Embedding
Epithet
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Euclid's Elements
Fundamental representation
Geometry
Half-integer
Hilbert space
Identity (mathematics)
Inference
Irreducible representation
Jones polynomial
Lie algebra
Linear combination
Linear extension
Linear independence
Linear map
Logic
Mathematical induction
Modular arithmetic
Monomial
Notation
Noun
Number form
Orthogonality
Outer product
Parameter
Perception
Permutation
Philosophy
Predicate (grammar)
Quantum group
Rectangle
Renormalization
Representation theory
Root of unity
Series (mathematics)
Sign (mathematics)
Special case
Spin network
Subset
Summation
Syllogism
Tensor
Tensor algebra
Tensor product
Tetrahedron
Theorem
Theory
Unit interval
Universal enveloping algebra
Variable (mathematics)
Weight (representation theory)
Product details
- ISBN 9780691027302
- Weight: 255g
- Dimensions: 152 x 235mm
- Publication Date: 31 Dec 1995
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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Addressing physicists and mathematicians alike, this book discusses the finite dimensional representation theory of sl(2), both classical and quantum. Covering representations of U(sl(2)), quantum sl(2), the quantum trace and color representations, and the Turaev-Viro invariant, this work is useful to graduate students and professionals. The classic subject of representations of U(sl(2)) is equivalent to the physicists' theory of quantum angular momentum. This material is developed in an elementary way using spin-networks and the Temperley-Lieb algebra to organize computations that have posed difficulties in earlier treatments of the subject. The emphasis is on the 6j-symbols and the identities among them, especially the Biedenharn-Elliott and orthogonality identities. The chapter on the quantum group Ub-3.0 qb0(sl(2)) develops the representation theory in strict analogy with the classical case, wherein the authors interpret the Kauffman bracket and the associated quantum spin-networks algebraically. The authors then explore instances where the quantum parameter q is a root of unity, which calls for a representation theory of a decidedly different flavor.
The theory in this case is developed, modulo the trace zero representations, in order to arrive at a finite theory suitable for topological applications. The Turaev-Viro invariant for 3-manifolds is defined combinatorially using the theory developed in the preceding chapters. Since the background from the classical, quantum, and quantum root of unity cases has been explained thoroughly, the definition of this invariant is completely contained and justified within the text.
J. Scott Carter is Associate Professor and Daniel E. Flath is Associate Professor, both in the Department of Mathematics at the University of South Alabama. Masahico Saito is Assistant Professor of Mathematics at the University of South Florida.
