Bicrossproduct structure of κ\kappa-Poincare group and non-commutative geometry

We show that the $\kappa$-deformed Poincar\'e quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct U(so(1,3))\cobicross T. The algebra is a semidirect product of the classical Lorentz group $so(1,3)$ acting in a deformed way on the momentum sector $T$. The novel feature is that the coalgebra is also semidirect, with a backreaction of the momentum sector on the Lorentz rotations. Using this, we show that the $\kappa$-Poincar\'e acts covariantly on a $\kappa$-Minkowski space, which we introduce. It turns out necessarily to be deformed and non-commutative. We also connect this algebra with a previous approach to Planck scale physics.Comment: 12 pages. Revision: minor typos correcte

Gauge theory on nonassociative spaces

We show how to do gauge theory on the octonions and other nonassociative algebras such as `fuzzy $R^4$' models proposed in string theory. We use the theory of quasialgebras obtained by cochain twist introduced previously. The gauge theory in this case is twisting-equivalent to usual gauge theory on the underlying classical space. We give a general U(1)-Yang-Mills example for any quasi-algebra and a full description of the moduli space of flat connections in this theory for the cube $Z_2^3$ and hence for the octonions. We also obtain further results about the octonions themselves; an explicit Moyal-product description of them as a nonassociative quantisation of functions on the cube, and a characterisation of their cochain twist as invariant under Fourier transform.Comment: 24 pages latex, two .eps figure

Quasialgebra structure of the octonions

We show that the octonions are a twisting of the group algebra of Z_2 x Z_2 x Z_2 in the quasitensor category of representations of a quasi-Hopf algebra associated to a group 3-cocycle. We consider general quasi-associative algebras of this type and some general constructions for them, including quasi-linear algebra and representation theory, and an automorphism quasi-Hopf algebra. Other examples include the higher 2^n-onion Cayley algebras and examples associated to Hadamard matrices.Comment: 34 pages LATE

Braided Cyclic Cocycles and Non-Associative Geometry

We use monoidal category methods to study the noncommutative geometry of nonassociative algebras obtained by a Drinfeld-type cochain twist. These are the so-called quasialgebras and include the octonions as braided-commutative but nonassociative coordinate rings, as well as quasialgebra versions \CC_{q}(G) of the standard q-deformation quantum groups. We introduce the notion of ribbon algebras in the category, which are algebras equipped with a suitable generalised automorphism $\sigma$, and obtain the required generalisation of cyclic cohomology. We show that this \emph{braided cyclic cocohomology} is invariant under a cochain twist. We also extend to our generalisation the relation between cyclic cohomology and differential calculus on the ribbon quasialgebra. The paper includes differential calculus and cyclic cocycles on the octonions as a finite nonassociative geometry, as well as the algebraic noncommutative torus as an associative example.Comment: 36 pages latex, 9 figure

Towards Spinfoam Cosmology

We compute the transition amplitude between coherent quantum-states of geometry peaked on homogeneous isotropic metrics. We use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in 1/volume. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex yields the Friedmann equation in the appropriate limit.Comment: 8 page

Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups $U_q(g)$. They have the same FRT generators $l^\pm$ but a matrix braided-coproduct \und\Delta L=L\und\tens L where $L=l^+Sl^-$, and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices $BM_q(2)$; it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum double D(\usl) (also known as the `quantum Lorentz group') is the semidirect product as an algebra of two copies of \usl, and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum groups and their semi-classical limits as doubles of the Lie algebras of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction

Dopamine receptors gene expression in male rat hippocampus after administration of MDMA (Ecstasy) [La Expresión Génica de Receptores de Dopamina en el Hipocampo de Ratas Macho Después de la Administración de MDMA (Éxtasis)]

Ecstasy is one of the most popular amusing drugs among young people. Documents indicate some effects of Ecstasy on hippocampus and close relations between dopaminergic functions with reward learning. Therefore, the aim of this study was evaluation of the chronic effects of Ecstasy on memory in male Wistar rats and determination of dopamine receptors' gene expression in hippocampus. Forty adult male Wistar rats randomly distributed in five groups: Control, sham (received 1 ml/kg 0.9 saline) and three experimental groups were: Exp. 1 (2.5 mg/kg), Exp. 2 (5 mg/kg), and Exp. 3 (10 mg/kg) received MDMA intraperitoneally once every 7 days (3 times a day, 3 hours apart) for 4 weeks. Before the first injection animals trained in Shuttle Box memory and tested after the last injection. 24 hours after the final testing, brains of rats were dissected and hippocampus was removed and homogenized. After total RNA extraction and cDNA synthesis, expression of dopamine receptor genes in the hippocampus determined with Real-Time PCR. Our results showed that 2.5 and 5 mg/kg MDMA-treated groups had memory impairment. Also we found that MDMA increased the mRNA expression of dopamine receptors in hippocampus and the highest increase found in dopamine D1 receptors in the 5 mg/kg experimental group. We concluded that low doses of Ecstasy could increase Dopamine takers gene expression in hippocampus and disorder avoidance memory. But in high doses the increase in Dopamine takers gene expression was not as much as that in low doses and avoidance memory disorder was not observed. © 2015, Universidad de la Frontera. All rights reserved

Bicrossproduct structure of the null-plane quantum Poincare algebra

A nonlinear change of basis allows to show that the non-standard quantum deformation of the (3+1) Poincare algebra has a bicrossproduct structure. Quantum universal R-matrix, Pauli-Lubanski and mass operators are presented in the new basis.Comment: 7 pages, LaTe