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1.
Steffen König 《Inventiones Mathematicae》1997,127(3):481-488
A criterion is given to show that a –algebra is quasi–hereditary if it can be defined over an integral domain , and if there is a certain commutative semisimple subalgebra satisfying a technical but easily verified condition (which
roughly states that over the field of fractions of , the formal characters of the semisimple –algebra generated by the –algebra defining satisfy an ordering condition). This applies in particular to Schur algebras (where various proofs of quasi–hereditary are
known, by de Concini, Eisenbud and Procesi, by Donkin, by Parshall, and by J.A. Green), generalized Schur algebras (covering
a result of Donkin), –Schur algebras (Dipper and James, Parshall and Wang), and Temperley–Lieb algebras (Westbury). The second application of this
point of view is an abstract straightening formula for the algebras satisfying the assumptions of the first theorem.
Oblatum 27-III-1995 & 18-IV-1996 相似文献
2.
Takahiro SUDO 《数学学报(英文版)》2007,23(7):1337-1340
We study K-theory of continuous deformations of C*-algebras to obtain that their K-theory is the same as that of the fiber at zero. We also consider continuous or discontinuous deformations of Cuntz and Toeplitz algebras. 相似文献
3.
Bounded commutative residuated lattice ordered monoids (Rℓ-monoids) are a common generalization of, e.g., Heyting algebras and BL-algebras, i.e., algebras of intuitionistic logic and basic fuzzy logic, respectively. Modal operators (special cases of closure
operators) on Heyting algebras were studied in [MacNAB, D. S.: Modal operators on Heyting algebras, Algebra Universalis 12 (1981), 5–29] and on MV-algebras in [HARLENDEROVá,M.—RACHŮNEK, J.: Modal operators on MV-algebras, Math. Bohem. 131 (2006), 39–48]. In the paper we generalize the notion of a modal operator for general bounded commutative Rℓ-monoids and investigate their properties also for certain derived algebras.
The first author was supported by the Council of Czech Government, MSM 6198959214. 相似文献
4.
I. Heckenberger 《Algebras and Representation Theory》2008,11(2):115-132
The concept of arithmetic root systems is introduced. It is shown that there is a one-to-one correspondence between arithmetic
root systems and Nichols algebras of diagonal type having a finite set of (restricted) Poincaré–Birkhoff–Witt generators.
This has strong consequences for both objects. As an application all rank 2 Nichols algebras of diagonal type having a finite
set of (restricted) Poincaré–Birkhoff–Witt generators are determined.
Supported by the European Community under a Marie Curie Intra-European Fellowship. 相似文献
5.
J.-L. Waldspurger 《Mathematische Annalen》2009,343(1):103-174
In order to use the trace formula of Arthur–Selberg in the twisted case, we need to prove the “twisted weighted fundamental
lemma”, that is a sophisticated version of the fundamental lemma. Here, we prove that this twisted weighted fundamental lemma
follows from two others lemmas, where the torsion has disappeared: the weighted fundamental lemma for Lie algebras and a “non-standard
weighted fundamental lemma”, concerning Lie algebras too. 相似文献
6.
We prove, constructively, that the Loomis–Sikorski Theorem for σ-complete Boolean algebras follows from a representation theorem
for Archimedean vector lattices and a constructive representation of Boolean algebras as spaces of Carathéodory place functions.
We also prove a constructive subdirect product representation theorem for arbitrary partially ordered vector spaces.
Received August 10, 2006; accepted in final form May 30, 2007. 相似文献
7.
We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras
which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras
defined over fields of characteristic zero are now known in principle.
Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002 相似文献
8.
We consider the algebras Λ which satisfy the property that for each indecomposable module X, either its projective dimension pdΛ
X is at most one or its injective dimension idΛ
X is at most one. This clearly generalizes the so-called quasitilted algebras introduced by Happel–Reiten–Smal?. We show that
some of the niciest features for this latter class of algebras can be generalized to the case we are considering, in particular
the existence of a trisection in its module category.
Received: 26 August 1998 相似文献
9.
Vladimir V. Kisil 《Advances in Applied Clifford Algebras》2007,17(1):59-70
This is an implementation of the Fillmore–Springer–Cnops construction (FSCc) based on the Clifford algebra capacities [10]
of the
GiNaC computer algebra system. FSCc linearises the linear-fraction action of the M?bius group. This turns to be very useful in
several theoretical and applied fields including engineering.
The core of this realisation of FSCc is done for an arbitrary dimension, while a subclass for two dimensional cycles add some
2D-specific routines including a visualisation to PostScript files through the
MetaPost or
Asymptote software.
This library is a backbone of many result published in [9], which serve as illustrations of its usage. It can be ported (with
various level of required changes) to other CAS with Clifford algebras capabilities. 相似文献
10.
In this paper we introduce the notion of generalized implication for lattices, as a binary function ⇒ that maps every pair of elements of a lattice to an ideal. We prove that a bounded lattice
A is distributive if and only if there exists a generalized implication ⇒ defined in A satisfying certain conditions, and we study the class of bounded distributive lattices A endowed with a generalized implication as a common abstraction of the notions of annihilator (Mandelker, Duke Math J 37:377–386,
1970), Quasi-modal algebras (Celani, Math Bohem 126:721–736, 2001), and weakly Heyting algebras (Celani and Jansana, Math Log Q 51:219–246, 2005). We introduce the suitable notions of morphisms in order to obtain a category, as well as the corresponding notion of congruence.
We develop a Priestley style topological duality for the bounded distributive lattices with a generalized implication. This
duality generalizes the duality given in Celani and Jansana (Math Log Q 51:219–246, 2005) for weakly Heyting algebras and the duality given in Celani (Math Bohem 126:721–736, 2001) for Quasi-modal algebras. 相似文献
11.
We completely classify the real root subsystems of root systems of loop algebras of Kac–Moody Lie algebras. This classification
involves new notions of “admissible subgroups” of the coweight lattice of a root system Ψ, and “scaling functions” on Ψ. Our
results generalise and simplify earlier work on subsystems of real affine root systems. 相似文献
12.
13.
We study the behavior of the Etingof–Kazhdan quantization functors under the natural duality operations of Lie bialgebras
and Hopf algebras. In particular, we prove that these functors are “compatible with duality”, i.e., they commute with the
operation of duality followed by replacing the coproduct by its opposite. We then show that any quantization functor with
this property also commutes with the operation of taking doubles. As an application, we show that the Etingof–Kazhdan quantizations
of some affine Lie superalgebras coincide with their Drinfeld–Jimbo-type quantizations.
To the memory of Paulette Libermann (1919–2007) 相似文献
14.
E. I. Zelenov 《Theoretical and Mathematical Physics》2008,157(3):1707-1712
We consider C*-algebras of commutation relations over the fields ℚ
p, p = 2, 3, 5, …, ∞. We describe all the irreducible separable representations of these algebras. We prove that the algebras
are not isomorphic at different p.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 406–412, December, 2008. 相似文献
15.
Claus Michael Ringel 《Archiv der Mathematik》2008,91(3):218-225
We are going to determine the self-injective cluster-tilted algebras. All are of finite representation type and special biserial.
There are two different classes. The first class are the self-injective serial (or Nakayama) algebras with n ≥ 3 simple modules and Loewy length n–1. The second class of algebras has an even number 2m of simple modules; m indecomposable projective modules have length 3, the remaining m have length m + 1.
Received: 28 May 2007 相似文献
16.
Daniel Beltiţa 《Mathematische Annalen》2002,324(2):405-429
The aim of the paper is to investigate spectral properties of the Lie algebras corresponding to the symmetry groups of certain
flags of vector bundles over a compact space. Under natural hypotheses, such Lie algebras are solvable, being in general infinite
dimensional. The spectral theory of finite-dimensional solvable Lie algebras of operators is extended to this natural class
of infinite-dimensional solvable Lie algebras. The discussion uses the language of continuous fields of -algebras. The flag manifolds in -algebraic framework are naturally involved here, they providing the basic method for obtaining flags of vector bundles.
Received: 8 October 2001 / Revised version: 4 February 2002 / Published online: 6 August 2002
Research supported from the contract ICA1–CT–2000–70022 with the European Commission. 相似文献
17.
John Enyang 《Journal of Algebraic Combinatorics》2007,26(3):291-341
A construction of bases for cell modules of the Birman–Murakami–Wenzl (or B–M–W) algebra B
n
(q,r) by lifting bases for cell modules of B
n−1(q,r) is given. By iterating this procedure, we produce cellular bases for B–M–W algebras on which a large Abelian subalgebra,
generated by elements which generalise the Jucys–Murphy elements from the representation theory of the Iwahori–Hecke algebra
of the symmetric group, acts triangularly. The triangular action of this Abelian subalgebra is used to provide explicit criteria,
in terms of the defining parameters q and r, for B–M–W algebras to be semisimple. The aforementioned constructions provide generalisations, to the algebras under consideration
here, of certain results from the Specht module theory of the Iwahori–Hecke algebra of the symmetric group.
Research supported by Japan Society for Promotion of Science. 相似文献
18.
Vladimir Dotsenko 《Selecta Mathematica, New Series》2009,14(2):229-245
We introduce several associative algebras and families of vector spaces associated to these algebras. Using lattice vertex
operators, we obtain dimension and character formulae for these spaces. In particular, we define a family of representations
of symmetric groups which turn out to be isomorphic to parking function modules. We also construct families of vector spaces
whose dimensions are Catalan numbers and Fuss–Catalan numbers respectively. Conjecturally, these spaces are related to spaces
of global sections of vector bundles on (zero fibres of) Hilbert schemes and representations of rational Cherednik algebras.
相似文献
19.
We investigate regular hyperbolic subalgebras of hyperbolic Kac–Moody algebras via their Weyl groups. We classify all subgroup
relations between Weyl groups of hyperbolic Kac–Moody algebras, and show that for every pair of a group and subgroup there
exists at least one corresponding pair of algebra and subalgebra. We find all types of regular hyperbolic subalgebras for
a given hyperbolic Kac–Moody algebra, and present a finite algorithm classifying all embeddings. 相似文献
20.
Changhe Liu Hongwei Liu Xinze Liu 《Journal of Optimization Theory and Applications》2012,154(3):949-965
This paper presents an extension of the variant of Mehrotra’s predictor–corrector algorithm which was proposed by Salahi and Mahdavi-Amiri (Appl. Math. Comput. 183:646–658, 2006) for linear programming to symmetric cones. This algorithm incorporates a safeguard in Mehrotra’s original predictor–corrector algorithm, which keeps the iterates in the prescribed neighborhood and allows us to get a reasonably large step size. In our algorithm, the safeguard strategy is not necessarily used when the affine scaling step behaves poorly, which is different from the algorithm of Salahi and Mahdavi-Amiri. We slightly modify the maximum step size in the affine scaling step and extend the algorithm to symmetric cones using the machinery of Euclidean Jordan algebras. Based on the Nesterov–Todd direction, we show that the iteration-complexity bound of the proposed algorithm is , where r is the rank of the associated Euclidean Jordan algebras and ε>0 is the required precision. 相似文献