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- Lundström, Patrik, 1971-
(author)
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Self-dual Normal Integral Bases for Infinite Unramified Extensions
- 2002
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In: Journal of Number Theory. - 0022-314X .- 1096-1658. ; 97:2, s. 350-367
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Journal article (peer-reviewed)abstract
- We prove a generalization to infinite Galois extensions of local fields, of a classical result by Noether on the existence of normal integral bases for finite tamely ramified Galois extensions. We also prove a self-dual normal integral basis theorem for infinite unramified Galois field extensions of local fields with finite residue fields of characteristic different from 2. This generalizes a result by Fainsilber for the finite case. To do this, we obtain an injectivity result concerning pointed cohomology sets, defined by inverse limits of norm-one groups of free finite-dimensional algebras with involution over complete discrete valuation rings.
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- Mazorchuk, Volodymyr, et al.
(author)
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Radical *-doubles of finite-dimensional algebras
- 2004
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In: Linear Algebra and its Applications. - : Elsevier BV. - 0024-3795. ; 390, s. 293-309
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Journal article (peer-reviewed)abstract
- The classification of the representation types for radical doubles of finite-dimensional algebras over the field of complex numbers was discussed. For the usal doubling, independent adjoints were added to all elements of original algebra where as for the radical doubling independent adjoints were added to the elements from the jacobsan radical of the algebra. The main advantange of the new construction is the representation type of the radical doubles happens to be a Mortia invariant of the original algebra. The result shows a tame-wild dichotomy for the given problem.
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- Svensson, Christian, et al.
(author)
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Dynamical systems associated with crossed products
- 2009
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In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications. - : Springer. - 0167-8019 .- 1572-9036. ; 108:3, s. 547-559
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Journal article (peer-reviewed)abstract
- In this paper, we consider both algebraic crossed products of commutative complex algebras A with the integers under an automorphism of A, and Banach algebra crossed products of commutative C*-algebras A with the integers under an automorphism of A. We investigate, in particular, connections between algebraic properties of these crossed products and topological properties of naturally associated dynamical systems. For example, we draw conclusions about the ideal structure of the crossed product by investigating the dynamics of such a system. To begin with, we recall results in this direction in the context of an algebraic crossed product and give simplified proofs of generalizations of some of these results. We also investigate new questions, for example about ideal intersection properties of algebras properly between the coefficient algebra A and its commutant A'. Furthermore, we introduce a Banach algebra crossed product and study the relation between the structure of this algebra and the topological dynamics of a naturally associated system.
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- Darpö, Erik
(author)
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Normal forms for the G2-action on the real symmetric 7 × 7-matrices by conjugation
- 2007
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In: Journal of Algebra. - : Elsevier BV. - 0021-8693 .- 1090-266X. ; 312:2, s. 668-688
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Journal article (peer-reviewed)abstract
- The exceptional Lie group G(2) subset of O-7 (R) acts on the set of real symmetric 7 x 7-matrices by conjugation. We solve the normal form problem for this group action. In view of the earlier results [G.M. Benkart, D.J. Britten, J.M. Osbom, Real flexible division algebras, Canad. J. Math. 34 (1982) 550-588; J.A. Cuenca Mira, R. De Los Santos Villodres, A. Kaidi, A. Rochdi, Real quadratic flexible division algebras, Linear Algebra Appl. 290 (1999) 1-22; E. Darpb, On the classification of the real flexible division algebras, Colloq. Math. 105 (1) (2006) 1-17], this gives rise to a classification of all finite-dimensional real flexible division algebras. By a classification is meant a list of pairwise non-isomorphic algebras, exhausting all isomorphism classes. We also give a parametrisation of the set of all real symmetric matrices, based on eigen values.
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- Makhlouf, Abdenacer, et al.
(author)
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Hom-algebra structures
- 2008
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In: Journal of Generalized Lie Theory and Applications. - 1736-5279 .- 1736-4337. ; 2:2, s. 51-64
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Journal article (peer-reviewed)abstract
- A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov in [4] and extended by Larsson and Silvestrov to quasi-hom Lie and quasi-Lie algebras in [5, 6]. In this paper we introduce and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic structures which generalize the well known associative, Leibniz and Lie admissible algebras. Also, we characterize the flexible Hom-algebras in this case. We also explain some connections between Hom-Lie algebras and Santilli’s isotopies of associative and Lie algebras.
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