SU_q(2) quantum group applied to spin-1/2 rotations yields non-commuting probability operators, an uncertainty principle for probabilities, and non-commutative rotation matrices between observers.
Majid,Foundations of Quantum Group Theory, Cambridge University Press (1995), 10.1017/CBO9780511613104
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For cocommutative Hopf dialgebras the set-like rack is naturally isomorphic to the conjugation rack of the group-like digroup, and every finite generalized digroup arises as the group-like elements of its digroup algebra.
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.
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Indefinite probabilities in quantum spacetime: A deepening of unpredictability
SU_q(2) quantum group applied to spin-1/2 rotations yields non-commuting probability operators, an uncertainty principle for probabilities, and non-commutative rotation matrices between observers.
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Cocommutative Hopf Dialgebras and Rack Combinatorics
For cocommutative Hopf dialgebras the set-like rack is naturally isomorphic to the conjugation rack of the group-like digroup, and every finite generalized digroup arises as the group-like elements of its digroup algebra.
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Weyl asymptotic formulas in the nilpotent Lie group setting
Spectral asymptotics for negative fractional powers of hypoelliptic operators on graded Lie groups generalize Birman-Solomyak and imply a version of Connes' integration formula.