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991.
Gabriel Bengochea 《代数通讯》2013,41(7):3086-3095
We prove that the cofinite dual of the Hopf algebra of polynomials in several variables can be represented as a Hopf algebra ? of exponential polynomials that contains the polynomials as a Hopf subalgebra. We also present some algebras isomorphic to ? whose elements are rational functions or multi-sequences. 相似文献
992.
993.
Alexey Kuz'min 《代数通讯》2013,41(8):3169-3189
Since 1976, it is known from the paper by V. P. Belkin that the variety RA2 of right alternative metabelian (solvable of index 2) algebras over an arbitrary field is not Spechtian (contains nonfinitely based subvarieties). In 2005, S. V. Pchelintsev proved that the variety generated by the Grassmann RA2-algebra of finite rank r over a field ?, for char(?) ≠ 2, is Spechtian iff r = 1. We construct a nonfinitely based variety 𝔐 generated by the Grassmann 𝒱-algebra of rank 2 of certain finitely based subvariety 𝒱 ? RA2 over a field ?, for char(?) ≠ 2, 3, such that 𝔐 can also be generated by the Grassmann envelope of a five-dimensional superalgebra with one-dimensional even part. 相似文献
994.
Christakis A. Pallikaros 《代数通讯》2013,41(11):4839-4859
995.
Xiaoping Xu 《代数通讯》2013,41(9):3589-3635
We find a new representation of the simple Lie algebra of type E 7 on the polynomial algebra in 27 variables. Using this representation and Shen's idea of mixed product, we construct a new functor from E 6-Mod to E 7-Mod. A condition for the functor to map a finite-dimensional irreducible E 6-module to an infinite-dimensional irreducible E 7-module is obtained. Our general framework also gives a direct polynomial extension from irreducible E 6-modules to irreducible E 7-modules, which can be used to derive Gel'fand–Zetlin bases for E 7 from those for E 6 that can be obtained from those for D 5 according to our earlier work. 相似文献
996.
We complement two papers on supertropical valuation theory ([11], [12]) by providing natural examples of m-valuations (= monoid valuations), and afterwards of supervaluations and transmissions between them. These supervaluations have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. We develop the basics of the theory of such semirings and transmissions. 相似文献
997.
Given two epimorphisms of algebras A ? B and C ? B, we consider the pullback R. We introduce a particular class of algebras, the tree oriented pullback, where there is a close relationship between the category of indecomposable modules of these algebras. This leads us to prove that if A and C are hereditary algebras, then R is a tilted algebra. 相似文献
998.
999.
Simon Lentner 《代数通讯》2013,41(10):4446-4470
We study realizations of root systems in possibly degenerate symplectic vector spaces over finite fields, up to symplectic isomorphisms. The main result of this article is the classification of such realizations for the field 𝔽2. Thereby, each root system requires a specific degree of degeneracy of the symplectic vector space. Our main motivation for this article is that for each such realization of a root system we can construct a Nichols algebra over a nonabelian group. 相似文献
1000.
Hossein Larki 《代数通讯》2013,41(12):5031-5058
For a (countable) graph E and a unital commutative ring R, we analyze the ideal structure of the Leavitt path algebra L R (E) introduced by Mark Tomforde. We first modify the definition of basic ideals and then develop the ideal characterization of Mark Tomforde. We also give necessary and sufficient conditions for the primeness and the primitivity of L R (E), and we then determine prime graded basic ideals and left (or right) primitive graded ideals of L R (E). In particular, when E satisfies Condition (K) and R is a field, they imply that the set of prime ideals and the set of primitive ideals of L R (E) coincide. 相似文献