doi: 10.1080/00927872.2013.816313pmid: N/A
Given a differential graded algebra 𝒞, we show that if the m-fold Massey product map H 1(𝒞) m → H 2(𝒞) is nonempty on every m-tuple, then it is single-valued on every m-tuple.
doi: 10.1080/00927872.2013.816314pmid: N/A
Inspired by rectilinearization theorems in subanalytic and o-minimal geometry, we define rings of multivariate Puiseux series induced by Weierstrass systems. In higher dimension, these rings lack good algebraic properties as Noetherianity. But we find a nice algebraic description as a twisted group ring.
Babaei, Massoumeh Nikkhah; Divaani-Aazar, Kamran
doi: 10.1080/00927872.2013.820734pmid: N/A
Let R be a commutative Noetherian ring and A an Artinian R-module. We prove that if A has finite Gorenstein injective dimension, then A possesses a Gorenstein injective envelope which is special and Artinian. This, in particular, yields that over a Gorenstein ring any Artinian module possesses a Gorenstein injective envelope which is special and Artinian.
Ahmadi, S. Ruhallah; Chaktoura, Martin; Szechtman, Fernando
doi: 10.1080/00927872.2013.839996pmid: N/A
Let f: V × V → F be a totally arbitrary bilinear form defined on a finite dimensional vector space V over a field F, and let L(f) be the subalgebra of 𝔤𝔩(V) of all skew-adjoint endomorphisms relative to f. Provided F is algebraically closed of characteristic not 2, we determine all f, up to equivalence, such that L(f) is reductive. As a consequence, we find, over an arbitrary field, necessary and sufficient conditions for L(f) to be simple, semisimple or isomorphic to 𝔰𝔩(n) for some n.
doi: 10.1080/00927872.2013.820735pmid: N/A
In this paper, we will show that if (R, 𝔪) is a quasi-unmixed local ring, I an 𝔪-primary ideal of R and ℛ𝒱(I) is the set of Rees valuations of I, then the number of minimal prime ideals in the 𝔪-adic completion of R equals exactly the number of equivalence classes on the set ℛ𝒱(I) under the equivalence relation ∼defined by: ν1 ∼ ν2 if there exist a constant c ≥ 1 such that for all x ∈ R, ν1(x) ≤ cν2(x) and ν2(x) ≤ cν1(x).
doi: 10.1080/00927872.2013.820736pmid: N/A
Chaput, Manivel, and Perrin proved in [3] a formula describing the quantum product by Schubert classes associated to cominuscule weights in a rational projective homogeneous space X. In the case where X has Picard rank one, we relate this formula to the stratification of X by P-orbits, where P is the parabolic subgroup associated to the cominuscule weight. We deduce a decomposition of the Hasse diagram of X, i.e., the diagram describing the cup-product with the hyperplane class. For all classical Grassmannians, we give a complete description of parabolic orbits associated to cominuscule weights, and we make the decomposition of the Hasse diagram explicit.
Bremner, Murray R.; Madariaga, Sara
doi: 10.1080/00927872.2013.820738pmid: N/A
We use computer algebra to determine all the multilinear polynomial identities of degree ≤7 satisfied by the trilinear operations (a·b)·c and a·(b·c) in the free dendriform dialgebra, where a·b is the pre-Lie or the pre-Jordan product. For the pre-Lie triple products, we obtain one identity in degree 3, and three independent identities in degree 5, and we show that every identity in degree 7 follows from the identities of lower degree. For the pre-Jordan triple products, there are no identities in degree 3, five independent identities in degree 5, and ten independent irreducible identities in degree 7. Our methods involve linear algebra on large matrices over finite fields, and the representation theory of the symmetric group.
Heidari, D.; Davvaz, B.; Modarres, S. M. S.
doi: 10.1080/00927872.2013.821314pmid: N/A
In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x, y) → x ○ y and (x, y) → x/y from H × H to 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset of H is a complete part, then the fundamental group of H is a topological group. It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett.
doi: 10.1080/00927872.2013.823500pmid: N/A
We determine finite simple groups which have a subgroup of index with exactly two distinct prime divisors. Then from this we derive a classification of primitive permutation groups of degree a product of two prime-powers.
doi: 10.1080/00927872.2013.823546pmid: N/A
The Hirokado variety is a Calabi–Yau threefold in characteristic 3 that is not liftable either to characteristic 0 or the ring W 2 of the second Witt vectors. Although Deligne–Illusie–Raynaud type Kodaira vanishing cannot be applied, we show that H 1(X, L −1) = 0, for an ample line bundle such that L 3 has a non-trivial global section, holds for this variety.
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