10,350 research outputs found
Classification of finite irreducible modules over the Lie conformal superalgebra CK6
We classify all continuous degenerate irreducible modules over the
exceptional linearly compact Lie superalgebra E(1, 6), and all finite
degenerate irreducible modules over the exceptional Lie conformal superalgebra
CK6, for which E(1, 6) is the annihilation algebra
Homalg: A meta-package for homological algebra
The central notion of this work is that of a functor between categories of
finitely presented modules over so-called computable rings, i.e. rings R where
one can algorithmically solve inhomogeneous linear equations with coefficients
in R. The paper describes a way allowing one to realize such functors, e.g.
Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra
system. Once this is achieved, one can compose and derive functors and even
iterate this process without the need of any specific knowledge of these
functors. These ideas are realized in the ring independent package homalg. It
is designed to extend any computer algebra software implementing the
arithmetics of a computable ring R, as soon as the latter contains algorithms
to solve inhomogeneous linear equations with coefficients in R. Beside
explaining how this suffices, the paper describes the nature of the extensions
provided by homalg.Comment: clarified some points, added references and more interesting example
Conley: Computing connection matrices in Maple
In this work we announce the Maple package conley to compute connection and
C-connection matrices. conley is based on our abstract homological algebra
package homalg. We emphasize that the notion of braids is irrelevant for the
definition and for the computation of such matrices. We introduce the notion of
triangles that suffices to state the definition of (C)-connection matrices. The
notion of octahedra, which is equivalent to that of braids is also introduced.Comment: conley is based on the package homalg: math.AC/0701146, corrected the
false "counter example
Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras
The present text surveys some relevant situations and results where basic
Module Theory interacts with computational aspects of operator algebras. We
tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be
published in Lecture Notes in Computer Scienc
Mutant knots with symmetry
Mutant knots, in the sense of Conway, are known to share the same Homfly
polynomial. Their 2-string satellites also share the same Homfly polynomial,
but in general their m-string satellites can have different Homfly polynomials
for m>2. We show that, under conditions of extra symmetry on the constituent
2-tangles, the directed m-string satellites of mutants share the same Homfly
polynomial for m<6 in general, and for all choices of m when the satellite is
based on a cable knot pattern.
We give examples of mutants with extra symmetry whose Homfly polynomials of
some 6-string satellites are different, by comparing their quantum sl(3)
invariants.Comment: 15 page
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