We provide a necessary and sufficient condition for a type D Temperley-Lieb algebra TLD
n
(
δ
) being semi-simple by studying branching rule for cell modules. As a byproduct, our result is used to ...study the so-called forked Temperley-Lieb algebra, which is a quotient algebra of TLD
n
(
δ
).
We study the Jacobson radical of the semicrossed product 𝒜 ×α
P when 𝒜 is a simple C*-algebra and P is either a semigroup contained in an abelian group or a free semigroup. A full characterization ...is obtained for a large subset of these semicrossed products and we apply our results to a number of examples.
On étudie dans un cadre abstrait des critères de semi-simplicité pour des représentations l-adiques de groupes profinis. On applique les résultats obtenus pour montrer que les relations ...d'Eichler-Shimura généralisées entraînent la semi-simplicitéde certaines représentations galoisiennes non triviales qui apparaissent dans la cohomologie des variétés de Shimura unitaires. Les résultats les plus intéressants sont obtenus pour les variétés de Shimura unitaires de signature $(n,0)^a \times (n-1,1)^b \times (1,n-1)^c \times (0,n)^d$.
We prove several abstract criteria for semi-simplicity of l-adic representations for profinite groups. As an application, we show that generalised Eichler-Shimura relations imply the semi-simplicity of a non-trivial subspace of middle cohomology of unitary Shimura varieties. The most complete results are obtained for unitary Shimura varieties of signature $(n,0)^a \times (n-1,1)^b \times (1,n-1)^c \times (0,n)^d$.
The Tate conjecture has two parts: i) Tate classes are linear combination of algebraic classes, ii) semisimplicity of Galois representations (for smooth projective varieties). B. Moonen proved that ...i) implies ii) in characteristic 0, using p-adic Hodge theory.
We show that an unconditional result lies behind this implication: the observability of arithmetic monodromy groups of geometric origin (in any characteristic) - which leads to a sharpening of Moonen's result.
We also discuss another aspect of the Tate conjecture related to the transcendence of p-adic periods.
The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians IG(2, 2n). We show that these rings are regular. In particular, by “generic smoothness”, we obtain ...a conceptual proof of generic semisimplicity of the big quantum cohomology for IG(2, 2n). Further, by a general result of Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type An−1. By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on IG(2, 2n). Such a collection is constructed in the appendix by Alexander Kuznetsov.
Quasi *-algebras form an essential class of partial *-algebras, which are algebras of unbounded operators. In this work, we aim to construct tensor products of normed, respectively Banach quasi ...*-algebras, and study their capacity to preserve some important properties of their tensor factors, like for instance, *-semisimplicity and full representability.
Commutative Hilbertian Frobenius algebras are those commutative semigroup objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the ...Frobenius compatibility relation, that is, this adjoint "comultiplication" is a bimodule map. In this note we show that the Frobenius relation forces the multiplication operators to be normal. We then prove that these algebras have a strong Wedderburn decomposition where the (ortho)complement of the Jacobson radical or equivalently of the annihilator, is the closure of the linear span of elements which essentially are the non-trivial characters. As a consequence such an algebra is semisimple if, and only if, its multiplication has a dense range. In particular every commutative special Hilbertian Frobenius algebra, that is, with a coisometric multiplication, is semisimple. Moreover we characterize from a setting a priori free of an involution, Ambrose's commutative
-algebras as the underlying algebras of Hilbertian Frobenius algebras. Extending a known result in the finite-dimensional situation, we prove that the structures of such Frobenius algebras on a given Hilbert space are in one-to-one correspondence with its bounded above orthogonal sets. We show, moreover, that the category of commutative Hilbertian Frobenius algebras is dually equivalent to a category of pointed sets.
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