7,359 research outputs found
Combinatorial operads from monoids
We introduce a functorial construction which, from a monoid, produces a
set-operad. We obtain new (symmetric or not) operads as suboperads or quotients
of the operads obtained from usual monoids such as the additive and
multiplicative monoids of integers and cyclic monoids. They involve various
familiar combinatorial objects: endofunctions, parking functions, packed words,
permutations, planar rooted trees, trees with a fixed arity, Schr\"oder trees,
Motzkin words, integer compositions, directed animals, and segmented integer
compositions. We also recover some already known (symmetric or not) operads:
the magmatic operad, the associative commutative operad, the diassociative
operad, and the triassociative operad. We provide presentations by generators
and relations of all constructed nonsymmetric operads.Comment: 42 pages. Complete version of the extended abstracts arXiv:1208.0920
and arXiv:1208.092
Algebraic Structures of Quantum Projective Field Theory Related to Fusion and Braiding. Hidden Additive Weight
The interaction of various algebraic structures describing fusion, braiding
and group symmetries in quantum projective field theory is an object of an
investigation in the paper. Structures of projective Zamolodchikov al- gebras,
their represntations, spherical correlation functions, correlation characters
and envelopping QPFT-operator algebras, projective \"W-algebras, shift
algebras, braiding admissible QPFT-operator algebras and projective
G-hypermultiplets are explored. It is proved (in the formalism of shift
algebras) that sl(2,C)-primary fields are characterized by their projective
weights and by the hidden additive weight, a hidden quantum number discovered
in the paper (some discussions on this fact and its possible relation to a
hidden 4-dimensional QFT maybe found in the note by S.Bychkov, S.Plotnikov and
D.Juriev, Uspekhi Matem. Nauk 47(3) (1992)[in Russian]). The special attention
is paid to various constructions of projective G-hyper- multiplets
(QPFT-operator algebras with G-symmetries).Comment: AMS-TEX, amsppt style, 16 pages, accepted for a publication in
J.MATH.PHYS. (Typographical errors are excluded
- …