65,217 research outputs found
The Yangian of sl(n|m) and the universal R-matrix
In this paper we study Yangians of sl(n|m) superalgebras. We derive the
universal R-matrix and evaluate it on the fundamental representation obtaining
the standard Yang R-matrix with unitary dressing factors. For m=0, we directly
recover up to a CDD factor the well-known S-matrices for relativistic
integrable models with su(N) symmetry. Hence, the universal R-matrix found
provides an abstract plug-in formula, which leads to results obeying
fundamental physical constraints: crossing symmetry, unitrarity and the
Yang-Baxter equation. This implies that the Yangian double unifies all desired
symmetries into one algebraic structure. In particular, our analysis is valid
in the case of sl(n|n), where one has to extend the algebra by an additional
generator leading to the algebra gl(n|n). We find two-parameter families of
scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure
Solving order constraints in logarithmic space.
We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space
Manifestly T-dual formulation of AdS space
We present a manifestly T-dual formulation of curved spaces such as an AdS
space. For group manifolds related by the orthogonal vielbein fields the three
form H=dB in the doubled space is universal at least locally. We construct an
affine nondegenerate doubled bosonic AdS algebra to define the AdS space with
the Ramond-Ramond flux. The non-zero commutator of the left and right momenta
leads to that the left momentum is in an AdS space while the right momentum is
in a dS space. Dimensional reduction constraints and the physical AdS algebra
are shown to preserve all the doubled coordinates.Comment: 35 pages, v2: Explanation of the relation to other approaches, a
pedagogical review and references are added, to appear in JHE
Decomposable functions and universal C*-algebras
This paper deals with universal C\sp\*-algebras generated by matricial relations on the generators, for example, the universal C\sp\*-algebra with generators a\sb{ij}, 1 \leq i,j \leq n, subject to the condition that the matrix (a\sb{ij}) be normal and have spectrum in a designated compact subset of the complex plane.
The main thrust of the paper is to compute the K-groups of some of these C\sp\*-algebras and to determine when they contain non-trivial projections. In the above example, we show that the K-groups of the algebra coincide with the topological K-groups of the set . We show, in general, that if the algebra has a multiplicative linear functional, then the K-theory is independent of n, when the matricial constraints are fixed.
It is also shown that if the constraints are fixed and {\cal A}\sb n is the algebra with n\sp2 generators, then the tensor product of {\cal A}\sb n with the algebra M\sb n of complex n x n matrices is isomorphic to the free product of {\cal A}\sb1 with M\sb n.
Also in the example above, the algebra contains no non-trivial projections when n is not less than the number of connected components of . These results have also been extended to include the case in which the constraints are in several variables
On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds
We review the details of unconstrained Lagrangian formulations for Bose
particles propagated on an arbitrary dimensional flat space-time and described
by the unitary irreducible integer higher-spin representations of the Poincare
group subject to Young tableaux with rows. The procedure
is based on the construction of Verma modules and finding auxiliary oscillator
realizations for the symplectic algebra which encodes the second-class
operator constraints subsystem in the HS symmetry algebra. Application of an
universal BRST approach reproduces gauge-invariant Lagrangians with reducible
gauge symmetries describing the free dynamics of both massless and massive
bosonic fields of any spin with appropriate number of auxiliary fields.Comment: 8 pages, no figures, extended Contribution to the Proceedings of the
International Workshop "Supersymmetry and Quantum Symmetries" (SQS'2011, July
18- July 23, 2011, Dubna, Russia), v.2: 9 pages, 2 references with comments
in Introduction adde
Givental formula in terms of Virasoro operators
We present a conjecture that the universal enveloping algebra of differential
operators \frac{\p}{\p t_k} over coincides in the origin with
the universal enveloping algebra of the (Borel subalgebra of) Virasoro
generators from the Kontsevich model. Thus, we can decompose any
(pseudo)differential operator to a combination of the Virasoro operators. Using
this decomposition we present the r.h.s. of the Givental formula
math.AG/0008067 as a constant part of the differential operator we introduce.
In the case of studied in hep-th/0103254, the l.h.s. of the
Givental formula is a unit, which imposes certain constraints on this
differential operator. We explicitly check that these constraints are correct
up to . We also propose a conjecture of factorization modulo Hirota
equation of the differential operator introduced and check this conjecture with
the same accuracy.Comment: LaTeX, 11 pages, Some typos correcte
Towards an Efficient Evaluation of General Queries
Database applications often require to
evaluate queries containing quantifiers or disjunctions,
e.g., for handling general integrity constraints. Existing
efficient methods for processing quantifiers depart from the
relational model as they rely on non-algebraic procedures.
Looking at quantified query evaluation from a new angle,
we propose an approach to process quantifiers that makes
use of relational algebra operators only. Our approach
performs in two phases. The first phase normalizes the
queries producing a canonical form. This form permits to
improve the translation into relational algebra performed
during the second phase. The improved translation relies
on a new operator - the complement-join - that generalizes
the set difference, on algebraic expressions of universal
quantifiers that avoid the expensive division operator in
many cases, and on a special processing of disjunctions by
means of constrained outer-joins. Our method achieves an
efficiency at least comparable with that of previous
proposals, better in most cases. Furthermore, it is considerably
simpler to implement as it completely relies on
relational data structures and operators
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