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1.
The results of [7] and [2] gave a recursive construction for all quasi-hereditary and standardly stratified algebras starting with local algebras and suitable bimodules. Using the notion of stratifying pairs of subcategories, introduced in [3], we generalize these earlier results to construct recursively all CPS-stratified algebras. 相似文献
2.
《代数通讯》2013,41(5):1559-1573
ABSTRACT In this paper we point out that the “Process of standardization”, given in Dlab and Ringel (1992), and also the “Comparison method” given in Platzeck and Reiten (2001) can be generalized. To do so, we introduce the concept of relative projective stratifying system and prove a result from which the Theorem 2 in Dlab and Ringel (1992) and Proposition 2.1 in Ringel (1991) follows. 相似文献
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4.
A. Van Daele 《代数通讯》2013,41(6):2235-2249
We extend the Larson–Sweedler theorem to group-cograded multiplier Hopf algebras introduced in Abd El-hafez et al. (2004), by showing that a group-cograded multiplier bialgebra with finite-dimensional unital components is a group-cograded multiplier Hopf algebra if and only if it possesses a nondegenerate left cointegral. We also generalize the theory of multiplier Hopf algebras of discrete type in Van Daele and Zhang (1999) to group-cograded multiplier Hopf algebras. Our results are applicable to Hopf group-coalgebras in the sense of Turaev (2000). Finally, we study regular multiplier Hopf algebras of η -discrete type. 相似文献
5.
Qunhua Liu 《代数通讯》2013,41(7):2656-2676
We study Schur algebras of classical groups over an algebraically closed field of characteristic different from 2. We prove that Schur algebras are generalized Schur algebras (in Donkin's sense) in types A, C, and D, while this does not hold in type B. Consequently Schur algebras of types A, C, and D are integral quasi-hereditary by Donkin [7, 9]. By using the coalgebra approach we put Schur algebras of a fixed classical group into a certain inverse system. We find that the corresponding hyperalgebra is contained in the inverse limit as a subalgebra. Moreover in types A, C, and D, the surjections in the inverse systems are compatible with the integral quasi-hereditary structure of Schur algebras. 相似文献
6.
A. Shabanskaya 《代数通讯》2017,45(6):2633-2661
A sequence of nilpotent Leibniz algebras denoted by Nn,18 is introduced. Here n denotes the dimension of the algebra defined for n≥4; the first term in the sequence is ?18 in the list of four-dimensional nilpotent Leibniz algebras introduced by Albeverio et al. [4]. Then all possible right and left solvable indecomposable extensions over the field ? are constructed so that Nn,18 serves as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program established to classify solvable Lie algebras using special properties rather than trying to extend one dimension at a time. 相似文献
7.
David Nacin 《代数通讯》2018,46(3):1243-1251
The algebras A(Γ), where Γ is a directed layered graph, were first constructed by Gelfand et al. [5]. These algebras are generalizations of the algebras Qn, which are related to factorizations of non-commutative polynomials. It was originally conjectured that these algebras were Koszul. In 2008, Cassidy and Shelton found a counterexample to this claim, a non-Koszul A(Γ) corresponding to a graph Γ with 18 edges and 11 vertices. We produce an example of a directed layered graph Γ with 13 edges and 9 vertices, which produces a non-Koszul A(Γ). We also show this is the minimal example with this property. 相似文献
8.
Takahiko Furuya 《代数通讯》2013,41(8):2926-2942
Let Λ be a finite-dimensional (D, A)-stacked monomial algebra. In this article, we give necessary and sufficient conditions for the variety of a simple Λ-module to be nontrivial. This is then used to give structural information on the algebra Λ, as it is shown that if the variety of every simple module is nontrivial, then Λ is a D-Koszul monomial algebra. We also provide examples of (D, A)-stacked monomial algebras which are not self-injective but nevertheless satisfy the finite generation conditions (Fg1) and (Fg2) of [4], from which we can characterize all modules with trivial variety. 相似文献
9.
José Antonio Cuenca Mira 《代数通讯》2013,41(12):4057-4067
A well-known Ingelstam's Theorem asserts that every real Hilbert space A with an associative unital product satisfying ‖ xy‖ ≤ ‖ x‖ ‖ y‖ and ‖ 1‖ = 1 is isomorphic to the reals ?, or the complex numbers ?, or the quaternions ?. This note deals with a nonunital and nonassociative extension of the Ingelstam Theorem. So the assumptions about associativity and existence of unity are weakened to the existence of a nonzero central idempotent e such that ‖ ex‖ = ‖e‖ ‖ x‖ for all x, and that in A holds a determined kind of algebraic identity strictly weaker that alternativeness. We prove that, up to isomorphisms, there are only seven algebras satisfying these assumptions, even without the requirement of completeness. On the other hand, Section 3 presents another characterization of the obtained algebras with the flavor of one of the main theorems in Bhatt et al. (1998). 相似文献
10.
Fabrizio Zanello 《代数通讯》2013,41(4):1087-1091
The purpose of this note is to supply an upper and a lower bound (which are in general sharp) for the h-vector of a level algebra which is relatively compressed with respect to any arbitrary level algebra A. The useful concept of relatively compressed algebra was recently introduced in Migliore et al. (2005) (whose investigations mainly focused on the particular case of A a complete intersection). The key idea of this note is the simple observation that the level algebras which are relatively compressed with respect to A coincide (after an obvious isomorphism) with the generic level quotients of suitable truncations of A. Therefore, we are able to apply to relatively compressed algebras the main result of our recent work, Zanello (2007). 相似文献
11.
In ([11]), we have studied quadratic Leibniz algebras that are Leibniz algebras endowed with symmetric, nondegenerate, and associative (or invariant) bilinear forms. The nonanticommutativity of the Leibniz product gives rise to other types of invariance for a bilinear form defined on a Leibniz algebra: the left invariance, the right invariance. In this article, we study the structure of Leibniz algebras endowed with nondegenerate, symmetric, and left (resp. right) invariant bilinear forms. In particular, the existence of such a bilinear form on a Leibniz algebra 𝔏 gives rise to a new algebra structure ☆ on the underlying vector space 𝔏. In this article, we study this new algebra, and we give information on the structure of this type of algebras by using some extensions introduced in [11]. In particular, we improve the results obtained in [22]. 相似文献
12.
ABSTRACT We study self-dual coradically graded pointed Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras (van Oystaeyen and Zhang, 2004). The co-Gabriel Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional pointed Hopf algebras with self-dual graded versions are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider (2000) and may help to classify finite dimensional self-dual coradically graded pointed Hopf algebras. 相似文献
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N. S. Khripchenko 《代数通讯》2013,41(5):1670-1676
It is well known that incidence algebras can be defined only for locally finite partially ordered sets (Doubilet et al., 1972; Stanley 1986). At the same time, for example, the poset of cells of a noncompact cell partition of a topological space is not locally finite. On the other hand, some operations, such as the order sum and the order product (Stanley, 1986), do not save the locally finiteness. So it is natural to try to generalize the concept of incidence algebra. In this article, we consider the functions in two variables on an arbitrary poset (finitary series), for which the convolution operation is defined. We obtain the generalization of incidence algebra—finitary incidence algebra and describe its properties: invertibility, the Jackobson radical, idempotents, regular elements. As a consequence a positive solution of the isomorphism problem for such algebras is obtained. 相似文献
15.
Paula A. A. B. Carvalho 《代数通讯》2013,41(5):1622-1646
A generalization of down-up algebras was introduced by Cassidy and Shelton (2004), the so-called “generalized down-up algebras”. We describe the automorphism group of conformal Noetherian generalized down-up algebras L(f, r, s, γ) such that r is not a root of unity, listing explicitly the elements of the group. In the last section, we apply these results to Noetherian down-up algebras, thus obtaining a characterization of the automorphism group of Noetherian down-up algebras A(α, β, γ) for which the roots of the polynomial X 2 ? α X ? β are not both roots of unity. 相似文献
16.
Yanhua Ren 《代数通讯》2013,41(5):1510-1518
By using the generating sequence and relations given by Ringel for his Ringel–Hall algebra in [8], we give a Gröbner–Shirshov basis for quantum group of type G 2. 相似文献
17.
Gil Vernik 《代数通讯》2013,41(6):2150-2155
18.
Zhixiang Wu 《代数通讯》2013,41(9):3869-3897
In the present article, we introduce G-graded left symmetric H-pseudoalgebras, where G is a grading group, and H is a cocommutative Hopf algebra. Some results about associative H-pseudoalgebras in [23] are generalized. The commutator algebras of the G-graded left symmetric H-pseudo-algebras are Lie H-pseudoalgebras, which are classified when the grading group is trivial in [3]. We investigate the left symmetric structure of Lie H-pseudoalgebras W(𝔟), S(𝔟), and He defined in [3]. 相似文献
19.
Evgeny Chibrikov 《代数通讯》2013,41(11):4014-4035
Sabinin algebras are algebraic objects that capture the local structure of analytic loops in the same way in which Lie algebras capture the local structure of Lie groups. They were introduced by Sabinin and Mibeev [13]. In 1962, Shirshov [20] suggested a scheme for choosing bases of a free Lie algebra that generalizes the Hall and Lyndon–Shirshov bases. In this article, we generalize the Shirshov scheme for the case of Sabinin algebras. 相似文献
20.
In [7] we introduced the notion of full quivers of representations of algebras, which are more explicit than quivers of algebras, and better suited for algebras over finite fields. Here, we consider full quivers as a combinatorial tool in order to describe PI-varieties of algebras. We apply the theory to clarify the proofs of diverse topics in the literature: Determining which relatively free algebras are weakly Noetherian, determining when relatively free algebras are finitely presented, presenting a quick proof for the rationality of the Hilbert series of a relatively free PI-algebra, and explaining counterexamples to Specht's conjecture for varieties of Lie algebras. 相似文献