.
We study certain algebraic properties of the small quantum homology algebra for the class of symplectic toric Fano manifolds. In particular, we examine the semisimplicity of this algebra, and the ...more general property of containing a field as a direct summand. Our main result provides an easily verifiable sufficient condition for these properties which is independent of the symplectic form. Moreover, we answer two questions of Entov and Polterovich negatively by providing examples of toric Fano manifolds with non-semisimple quantum homology, and others in which the Calabi quasi-morphism is not unique.
Let
R be a hereditary, indecomposable, left pure-semisimple ring. We show that
R has finite representation type if and only if a certain finitely presented module is endofinite, namely, the tilting ...and cotilting module
W studied in L. Angeleri Hügel (2007)
2. We then apply the tilting and the cotilting functors to study the endomorphism ring of
W and its Auslander–Reiten components. Finally, we transfer this information to the category of right
R-modules.
It is known that the Frame number characterizes the semisimplicity of adjacency algebras of association schemes (see A. Hanaki, “Semisimplicity of adjacency algebras of association schemes”, J. ...Algebra, 225 (2000), 124–129). Coherent configurations are a generalization of association schemes. In this paper, we aim to extend this fact to coherent configurations.
In this paper, we give a recursive formula to compute the Gram determinant associated to each cell module of the cyclotomic BMW algebras
over an integral domain. As a by-product, we determine ...explicitly when
is semisimple over a field. This generalizes our previous result on Birman-Murakami-Wenzl algebras in Rui and Si (J Reine Angew Math 631:153–180,
2009
).
Partial Actions and Partial Fixed Rings Ávila, Jesús; Ferrero, Miguel; Lazzarin, João
Communications in algebra,
6/14/2010, Letnik:
38, Številka:
6
Journal Article
Recenzirano
In this article, we consider a partial action α of a finite group G on a ring R which possesses an enveloping action. Properties of the fixed subring R
α
are studied. Among other results, under some ...assumptions, we describe the prime radical, the Jacobson radical, and the upper nil radical. We also study semisimplicity, von Newmann regularity, and Goldie conditions.
We show that the representation, introduced by Lawrence and Krammer to show the linearity of the braid group, is generically irreducible. However, for some values of its two parameters when these are ...specialized to complex numbers, it becomes reducible. We construct a representation of degree
n
(
n
−
1
)
2
of the BMW algebra of type
A
n
−
1
. As a representation of the braid group on
n strands, it is equivalent to the Lawrence–Krammer representation where the two parameters of the BMW algebra are related to those appearing in the Lawrence–Krammer representation. We give the values of the parameters for which the representation is reducible and give the proper invariant subspaces in some cases. We use this representation to show that for these special values of the parameters, the BMW algebra of type
A
n
−
1
is not semisimple.
The unified treatment of the five module-theoretic notions, transfer, inflation, transport of structure by an isomorphism, deflation and restriction, is given by the theory of biset functors, ...introduced by Bouc. In this paper, we construct the algebra realizing biset functors as representations. The algebra has a presentation similar to the well-known Mackey algebra. We adopt some natural constructions from the theory of Mackey functors and give two new constructions of simple biset functors. We also obtain a criterion for semisimplicity in terms of the biset functor version of the mark homomorphism. The criterion has an elementary generalization to arbitrary finite-dimensional algebras over a field.
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