منابع مشابه
Double loop spaces, braided monoidal categories and algebraic 3-type of space
We show that the nerve of a braided monoidal category carries a natural action of a simplicial E2-operad and is thus up to group completion a double loop space. Shifting up dimension twice associates to each braided monoidal category a 1-reduced lax 3-category whose nerve realizes an explicit double delooping whenever all cells are invertible. We deduce that lax 3-groupoids are algebraic models...
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The notion of q-Brownian motion introduced by Majid is extended to braided spaces corresponding to a generic R-matrix, and combined with the theory of quantum probability. This leads to a deenition of diiusions on these spaces. The corresponding heat equations (diierence-diierential equations) are solved in terms of Appell polynomials (i.e. shifted moment systems). Some examples of interest for...
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We show that the space of long knots in an euclidean space of dimension larger than three is a double loop space, proving a conjecture by Sinha. We also construct a double loop space structure on framed long knots, and show that the map forgetting the framing is not a double loop map in odd dimension. However there is always such a map in the reverse direction expressing the double loop space o...
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∗-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include q-Minkowski and q-Euclidean spaces as additive braided groups. The duality between the ∗-braided groups of vectors and covectors is proved and some first applications to braided geometry are made.
متن کاملBraided products for quantum spaces
Attention is focused on quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. There are algebra isomorphisms that allow to identify quantum spaces with commutative coordinate algebras. This observation enables the realization of braiding mappings on commutative algebras. The aim of the article is to...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6614