## Probability on Algebraic Structures: AMS Special Session on Probability on Algebraic Structures, March 12-13, 1999, Gainesville, FloridaThis volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups. |

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### Contents

II Hypergroups | 71 |

III Symmetric Cones Wishart Distributions | 107 |

IV Quantum Groups Quantum Probability | 143 |

V Semigroups Matrices Applications | 193 |

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### Common terms and phrases

Accardi Ad-unipotent subgroup automorphism bialgebra Borel characterization classical version commutative compact subgroup connected Lie group contained contractive modulo converges weakly convolution semigroup Corollary defined denote dimensional element equation Euclidean exists exp L(S finite Fock space follows functions Gaussian given GL(n group G Haar measure Hence hypergroup implies independent int(W invariant Jordan algebra Jurek kernel Lemma Let G Letac Lévy processes Lie algebra linear locally compact group martingale Math matrices measure on G modulo a compact nilpotent Lie groups nondissipating probability measures operator polynomials positive probability measure problem proof Proposition prove quantum probability quantum stochastic random fields random variables relatively compact representation result s-stable satisfies second countable semigroup sequence SF(K simply connected stochastic calculus stochastic process strongly root compact subgroup of G subsemigroup subset supp symmetric cone Theorem 3.1 vector white noise Wishart distributions