Abstract. We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasihereditary algebra. In the special case of rigid symmetric algebras we show that they can be realized as centralizer subalgebras of symmetric quasi-hereditary algebras. We also show that the infinite-dimensional symmetric quasi-hereditary algebras we construct admit quasi-her...

We study the large scale geometry of the upper triangular subgroup of PSL2(Z[ 1 n ]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogue...

We present a formalism within which the relationship (discovered by Drinfel’d in [Dr1, Dr2]) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the Grothendieck-Teichmuller group becomes simple and natural, leading to a great simplification of Drinfel’d’s original work. In particular, we re-prove that rational associators exist and can be constructed iteratively.

Tokamak regimes with nearly zero or negative toroidal current in the central region (current hole) feature good plasma confinement properties and may be naturally attained in the advanced tokamak (AT) regime. On the other hand, quasi-steady-state AC plasma current operation in tokamaks relies upon the existence of current reversal equilibria with zero net toroidal current. In both cases a syste...

Normal modes, quasi-normal modes and super-radiant modes are studied to clarify the total dynamics for complex scalar fields in Kerr anti-de Sitter black hole spacetime. Orthonormal relations and quasi-orthonormal relations are obtained for normal modes and quasi-normal modes. Mode expansions are done and the conserved quantities are studied. Any modes are shown to be separated into two groups,...

We give precise formulae for the coeecients of Drin-feld's KZ associator in terms of iterated integrals over the unit interval. These formulae are used to calculate Kontsevich's universal knot invariant for (2; p)-torus knots up to the 4-th order. There are already several combinatorial descriptions of Kontsevich's universal knot invariant Ko] in terms of Drinfeld's work on quasi-triangular qua...