196 research outputs found
Non-abelian extensions of Rota-Baxter Lie algebras and inducibility of automorphisms
A Rota-Baxter Lie algebra is a Lie algebra
equipped with a Rota-Baxter operator . In this paper, we consider non-abelian extensions of a
Rota-Baxter Lie algebra by another Rota-Baxter Lie algebra
We define the non-abelian cohomology which classifies {equivalence classes of}
such extensions. Given a non-abelian extension
of Rota-Baxter Lie algebras, we also show that the obstruction for a pair of
Rota-Baxter automorphisms in to be induced by an automorphism in
lies in the cohomology group . As a byproduct, we obtain the Wells
short-exact sequence in the context of Rota-Baxter Lie algebras.Comment: Any comments/suggestions are welcom
Exact S-matrices for supersymmetric sigma models and the Potts model
We study the algebraic formulation of exact factorizable S-matrices for
integrable two-dimensional field theories. We show that different formulations
of the S-matrices for the Potts field theory are essentially equivalent, in the
sense that they can be expressed in the same way as elements of the
Temperley-Lieb algebra, in various representations. This enables us to
construct the S-matrices for certain nonlinear sigma models that are invariant
under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the
bulk and for the boundary, simply by using another representation of the same
algebra. These S-matrices represent the perturbation of the conformal theory at
theta=pi by a small change in the topological angle theta. The m=1, n=1 theory
has applications to the spin quantum Hall transition in disordered fermion
systems. We also find S-matrices describing the flow from weak to strong
coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma
models.Comment: 32 pages, 8 figure
Framization of the Temperley-Lieb Algebra
We propose a framization of the Temperley-Lieb algebra. The framization is a
procedure that can briefly be described as the adding of framing to a known
knot algebra in a way that is both algebraically consistent and topologically
meaningful. Our framization of the Temperley-Lieb algebra is defined as a
quotient of the Yokonuma-Hecke algebra. The main theorem provides necessary and
sufficient conditions for the Markov trace defined on the Yokonuma-Hecke
algebra to pass through to the quotient algebra. Using this we construct
1-variable invariants for classical knots and links, which, as we show, are not
topologically equivalent to the Jones polynomial.Comment: 30 page
Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
We disclose the mathematical structure underlying the gauge field sector of
the recently constructed non-abelian superconformal models in six spacetime
dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge
fields. We show that the algebraic consistency constraints governing this
system permit to define a Lie 3-algebra, generalizing the structural Lie
algebra of a standard Yang-Mills theory to the setting of a higher bundle.
Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type
operator Q, this higher bundle can be compactly described by means of a
Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to
the Lie 3-algebra and its base the odd tangent bundle of spacetime equipped
with the de Rham differential. The generalized Bianchi identities can then be
retrieved concisely from Q^2=0, which encode all the essence of the structural
identities. Gauge transformations are identified as vertical inner
automorphisms of such a bundle, their algebra being determined from a Q-derived
bracket.Comment: 51 pages, 3 figure
Convergence to the boundary for random walks on discrete quantum groups and monoidal categories
We study the problem of convergence to the boundary in the setting of random
walks on discrete quantum groups. Convergence to the boundary is established
for random walks on . Furthermore, we will define the
Martin boundary for random walks on C-tensor categories and give a
formulation for convergence to the boundary for such random walks. These
categorical definitions are shown to be compatible with the definitions in the
quantum group case. This implies that convergence to the boundary for random
walks on quantum groups is stable under monoidal equivalence.Comment: 67 pages; Shortened sections 2 and 5; Corrected Lemma 5.15; Corrected
several typo
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