ON BIALGEBRAS ASSOCIATED WITH PATHS AND ESSENTIAL PATHS ON ADE GRAPHS

@article{Coquereaux2005ONBA,
  title={ON BIALGEBRAS ASSOCIATED WITH PATHS AND ESSENTIAL PATHS ON ADE GRAPHS},
  author={R. Coquereaux and A. Garcia},
  journal={International Journal of Geometric Methods in Modern Physics},
  year={2005},
  volume={02},
  pages={441-466}
}
  • R. Coquereaux, A. Garcia
  • Published 2005
  • Mathematics, Physics
  • International Journal of Geometric Methods in Modern Physics
  • We define a graded multiplication on the vector space of essential paths on a graph G (a tree) and show that it is associative. In most interesting applications, this tree is an ADE Dynkin diagram. The vector space of length-preserving endomorphisms of essential paths has a grading obtained from the length of paths and possesses several interesting bialgebra structures. One of these, the Double Triangle Algebra (DTA) of A. Ocneanu, is a particular kind of quantum groupoid (a weak Hopf algebra… CONTINUE READING
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    References

    SHOWING 1-10 OF 16 REFERENCES
    On quantum symmetries of ADE graphs
    • 21
    • PDF
    Weak Hopf Algebras: I. Integral Theory and C-Structure
    • 392
    • PDF
    The many faces of Ocneanu cells
    • 130
    • PDF
    Axioms for Weak Bialgebras
    • 68
    • PDF
    A coassociativeC*-quantum group with nonintegral dimensions
    • 145
    • PDF
    The A-D-E classification of minimal andA1(1) conformal invariant theories
    • 460
    • Highly Influential
    The A2 Ocneanu quantum groupoid
    • 7
    • PDF