9,641 research outputs found
Consecutive Support: Better Be Close!
We propose a new measure of support (the number of occur- rences of a
pattern), in which instances are more important if they occur with a certain
frequency and close after each other in the stream of trans- actions. We will
explain this new consecutive support and discuss how patterns can be found
faster by pruning the search space, for instance using so-called parent support
recalculation. Both consecutiveness and the notion of hypercliques are
incorporated into the Eclat algorithm. Synthetic examples show how interesting
phenomena can now be discov- ered in the datasets. The new measure can be
applied in many areas, ranging from bio-informatics to trade, supermarkets, and
even law en- forcement. E.g., in bio-informatics it is important to find
patterns con- tained in many individuals, where patterns close together in one
chro- mosome are more significant.Comment: 10 page
Constructing homomorphisms between Verma modules
A practical method for constructing a nontrivial homomorphsim between Verma
modules is described.Comment: 15 pages, added references, some comments on the affine case, an
application concerning the construction of irreducible module
Computations with nilpotent orbits in SLA
We report on some computations with nilpotent orbits in simple Lie algebras
of exceptional type within the SLA package of GAP4. Concerning reachable
nilpotent orbits our computations firstly confirm the classification of such
orbits in Lie algebras of exceptional type by Elashvili and Grelaud, secondly
they answer a question by Panyushev, and thirdly they show in what way a recent
result of Yakimova for the Lie algebras of classical type extends to the
exceptional types. The second topic of this note concerns abelianizations of
centralizers of nilpotent elements. We give tables with their dimensions.Comment: This paper contains arXiv:1004.4061 [math.RA] (except the appendix
An algorithm to compute the canonical basis of an irreducible Uq(g)-module
An algorithm is described to compute the canonical basis of an irreducible
module over a quantized enveloping algebra of a finite-dimensional semisimple
Lie algebra. The algorithm works for modules that are constructed as a
submodule of a tensor product of modules with known canonical bases.Comment: 12 page
Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
First we describe the Skjelbred-Sund method for classifying nilpotent Lie
algebras. Then we use it to classify 6-dimensional nilpotent Lie algebras over
any field of characteristic not 2. The proof of this classification is
essentially constructive: for a given 6-dimensional nilpotent Lie algebra L,
following the steps of the proof, it is possible to find a Lie algebra M that
occurs in the list, and an isomorphism L --> M.Comment: 23 page
Classification of solvable Lie algebras
We illustrate some simple ideas that can be used for obtaining a
classification of small-dimensional solvable Lie algebras.Using these we obtain
the classification of 3 and 4 dimensional solvable Lie algebras (over fields of
any characteristic). Precise conditions for isomorphism are given.Comment: 16 page
Classification of nilpotent associative algebras of small dimension
We classify nilpotent associative algebras of dimensions up to 4 over any
field. This is done by constructing the nilpotent associative algebras as
central extensions of algebras of smaller dimension, analogous to methods known
for nilpotent Lie algebras
Closed subsets of root systems and regular subalgebras
We describe an algorithm for classifying the closed subsets of a root system,
up to conjugation by the associated Weyl group. Such a classification of an
irreducible root system is closely related to the classification of the regular
subalgebras, up to inner automorphism, of the corresponding simple Lie algebra.
We implement our algorithm to classify the closed subsets of the irreducible
root systems of ranks 3 through 7. We present a complete description of the
classification for the closed subsets of the rank 3 irreducible root system. We
employ this root system classification to classify all regular subalgebras of
the rank 3 simple Lie algebras. We present only summary data for the
classifications in higher ranks due to the large size of these classifications.
Our algorithm is implemented in the language of the computer algebra system
GAP
Constructing semisimple subalgebras of real semisimple Lie algebras
We consider the problem of constructing semisimple subalgebras of real
(semi-) simple Lie algebras. We develop computational methods that help to deal
with this problem. Our methods boil down to solving a set of polynomial
equations. In many cases the equations turn out to be sufficiently "pleasant"
to be able to solve them. In particular this is the case for S-subalgebras
irrep decompositions of interest for physical models
In this note we show how to obtain the projection matrix for the chain and we tabulate some decompositions of the symplectic algebra
representations into irreps of the subalgebra that are important
for various physical models
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