∗–Structures on Braided Spaces
نویسندگان
چکیده
∗-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.
منابع مشابه
Diiusions on Braided Spaces Ii Preliminaries Ii.1 Braided Spaces
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...
متن کاملBraided Diagram Groups and Local Similarity Groups
Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common characteristics: both act properly by isometries on CAT(0) cubical complexes, and certain groups in both classes have type F∞, for instance. Here we clarify the relati...
متن کاملClassifying Spaces for Braided Monoidal Categories and Lax Diagrams of Bicategories
This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy type of their classifying spaces. Bicategories (in particular monoidal categories) have well understood simple geometric realizations, and we here deal with homotopy types represented by lax diagrams of bicategories, that is, lax functors to the tricategory of bicategories. I...
متن کاملThe Erwin Schrr Odinger International Institute for Mathematical Physics Q{epsilon Tensor for Quantum and Braided Spaces Q-epsilon Tensor for Quantum and Braided Spaces
The machinery of braided geometry introduced previously is used now to construct thètotally antisymmetric tensor' on a general braided vector space determined by R-matrices. This includes natural q-Euclidean and q-Minkowski spaces. The formalism is completely covariant under the corresponding quantum group such as g SO q (4) or g SO q (1; 3). The Hodge operator and diierentials are also constru...
متن کاملq-EPSILON TENSOR FOR QUANTUM AND BRAIDED SPACES
The machinery of braided geometry introduced previously is used now to construct the ǫ ‘totally antisymmetric tensor’ on a general braided vector space determined by R-matrices. This includes natural q-Euclidean and q-Minkowski spaces. The formalism is completely covariant under the corresponding quantum group such as ̃ SOq(4) or ̃ SOq(1, 3). The Hodge ∗ operator and differentials are also cons...
متن کامل