We formulate sufficient conditions for the strong integrability of dressing cosets. provide several sigma-model backgrounds solving those conditions, some them are new and were not so far formulated as The models based on Drinfeld doubles having structure higher-order jet bundles quadratic Lie groups.

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations dualities, which is not immediately obvious. A prime example Scherk-Schwarz reductions double theory, have been shown to be one-to-one correspondence with Poisson-Lie T-duality. Here we demonstrate that this relation only the tip of iceberg. Currently, most general known...

We describe some improved techniques for the computation of short cosets. This speeds up the computation of Galois groups in magma.

An ordinary voltage graph embedding in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph G in a surface with voltage group A and a connected subgraph H of G, we define special subgroups of A that depend on H and show how cosets of these groups in A can be used to find topological information concerning the d...

The recent proposal (M Planat and M Kibler, Preprint 0807.3650 [quantph]) of representing Clifford quantum gates in terms of unitary reflections is revisited. In this essay, the geometry of a Clifford group G is expressed as a BN-pair, i.e. a pair of subgroups B and N that generate G, is such that intersection H = B ∩N is normal in G, the group W = N/H is a Coxeter group and two extra axioms ar...

Properties of a given symmetry group G are very important in investigation of a physical system invariant under its action. In the case of finite spin systems (magnetic rings, some planar macromolecules) the symmetry group is isomorphic with the dihedral group DN . In this paper group-theoretical ‘parameters’ of such groups are determined, especially decompositions of transitive representations...

For i = 1,2, let r j be a lattice in a connected Lie group G j , and let X j be a connected Lie subgroup of Gj . The double cosets rjg X j provide a foliation .9'; of the homogeneous space rj\Gj . Assume that XI and X2 are unimodular and that .91 has a dense leaf. If G I and G2 are semisimple groups to which the Mostow Rigidity Theorem applies, or are simply connected nilpotent groups (or are c...

Abstract Embeddings of the space barcodes in Euclidean spaces are unstable due to permutation bars a barcode. We use tools from geometric group theory produce stratification $${\mathcal {B}}_n$$ B n with n that takes into account these permutations. This gives insights ...