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| 2. |
- Tkachev, Vladimir G.
(författare)
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Disjoint minimal graphs
- 2009
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 0232-704X .- 1572-9060. ; 35:2, s. 139-155
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the number s(n) of disjoint minimal graphs supported on domains in R-n is bounded by e(n + 1)(2). In the two-dimensional case, we show that s(2) <= 3.
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| 3. |
- Arnlind, Joakim, et al.
(författare)
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Affine transformation crossed product type algebras and noncommutative surfaces
- 2009. - 503
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Ingår i: Operator structures and dynamical systems. - Providence, Rhode Island : American Mathematical Society (AMS). - 9780821847473 - 9780821881828 ; , s. 1-25
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Bokkapitel (refereegranskat)abstract
- Several classes of *-algebras associated to teh action of an affine transformation are considered, and an investigation of the interplay between the different classes is initiated. Connections are established that relate representations of *-algebras, geometry of algebraic surfaces, dynamics of affine transformations, graphs and algebras coming from a quantization procedure of Poisson structures. In particular, algebras related to surgaced being inverse images of fourth order polynomials (in ) are studied in detail, and a close link between representation theory and geometric properties is established for compact as well as non-compact surfaces.
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| 4. |
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| 5. |
- Sinel'shchikov, S., et al.
(författare)
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A quantum analogue of the bernstein functor
- 2007
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Ingår i: Journal of Lie Theory. - 0949-5932. ; 17:1, s. 73-89
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Tidskriftsartikel (refereegranskat)abstract
- We consider Knapp-Vogan Hecke algebras in the quantum group setting. This allows us to produce a quantum analogue of the Bernstein functor as a first step towards the cohomological induction for quantum groups.
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| 6. |
- Berglund, Alexander
(författare)
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Shellability and the strong gcd-condition
- 2009
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Ingår i: The Electronic Journal of Combinatorics. - 1097-1440 .- 1077-8926. ; 16:2
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Tidskriftsartikel (refereegranskat)abstract
- Shellability is a well-known combinatorial criterion on a simplicial complex for verifying that the associated Stanley-Reisner ring k[] is Cohen-Macaulay. Anotion familiar to commutative algebraists, but which has not received as muchattention from combinatorialists as the Cohen-Macaulay property, is the notion ofa Golod ring. Recently, J¨ollenbeck introduced a criterion on simplicial complexesreminiscent of shellability, called the strong gcd-condition, and he together with theauthor proved that it implies Golodness of the associated Stanley-Reisner ring. Thetwo algebraic notions were earlier tied together by Herzog, Reiner and Welker, whoshowed that if k[∨] is sequentially Cohen-Macaulay, where ∨ is the Alexanderdual of , then k[] is Golod. In this paper, we present a combinatorial companionof this result, namely that if ∨ is (non-pure) shellable then satisfies the stronggcd-condition. Moreover, we show that all implications just mentioned are strict ingeneral but that they are equivalences if is a flag complex.
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| 7. |
- Eriksson, Dennis, 1981, et al.
(författare)
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On the Brauer-Manin obstruction for zero-cycles on curves
- 2008
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Ingår i: Acta Arithmetica. - 1730-6264 .- 0065-1036. ; 136:2, s. 99-110
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Tidskriftsartikel (refereegranskat)abstract
- We wish to give a short elementary proof of S. Saito's result that the Brauer-Manin obstruction for zero-cycles of degree 1 is the only one for curves, supposing the finiteness of the Tate-Shafarevich-group $\sha^1(A)$ of the Jacobian variety. In fact we show that we only need a conjecturally finite part of the Brauer-group for this obstruction to be the only one. We also comment on the situation in higher dimensions.
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| 8. |
- Sakovich, Anna, 1982-, et al.
(författare)
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Harmonic morphisms from the classical compact semisimple Lie groups
- 2008
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Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 0232-704X .- 1572-9060. ; 33:4, s. 343-356
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we introduce a new method for manufacturing harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Lie groups SO( n), SU( n) and Sp( n) equipped with their standard Riemannian metrics. We develop a duality principle and show how this can be used to construct the first known examples of harmonic morphisms from the non-compact Lie groups SL(n)( R), SU*( 2n), Sp( n, R), SO*( 2n), SO( p, q), SU( p, q) and Sp( p, q) equipped with their standard dual semi-Riemannian metrics.
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| 9. |
- Sakovich, Anna, 1982-, et al.
(författare)
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Harmonic morphisms from the classical non-compact semisimple Lie groups
- 2009
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Ingår i: Differential geometry and its applications (Print). - : Elsevier BV. - 0926-2245 .- 1872-6984. ; 27:1, s. 47-63
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Tidskriftsartikel (refereegranskat)abstract
- We construct the first known complex-valued harmonic morphisms from the non-compact Lie groups SL(n) (R), SU*(2n) and Sp(n, R) equipped with their standard Riemannian metrics. We then introduce the notion of a bi-eigenfamily and employ this to construct the first known solutions on the non-compact Riemannian SO*(2n), SO(p, q), SU(p, q) and Sp(p, q). Applying a duality, principle we then show how to manufacture the first known complex-valued harmonic morphisms from the compact Lie groups SO(n), SU(n) and Sp(n) equipped with semi-Riemannian metrics.
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| 10. |
- Herschend, Martin, 1981-
(författare)
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On the Clebsch-Gordan problem for quiver representations
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- On the category of representations of a given quiver we define a tensor product point-wise and arrow-wise. The corresponding Clebsch-Gordan problem of how the tensor product of indecomposable representations decomposes into a direct sum of indecomposable representations is the topic of this thesis.The choice of tensor product is motivated by an investigation of possible ways to modify the classical tensor product from group representation theory to the case of quiver representations. It turns out that all of them yield tensor products which essentially are the same as the point-wise tensor product.We solve the Clebsch-Gordan problem for all Dynkin quivers of type A, D and E6, and provide explicit descriptions of their respective representation rings. Furthermore, we investigate how the tensor product interacts with Galois coverings. The results obtained are used to solve the Clebsch-Gordan problem for all extended Dynkin quivers of type Ãn and the double loop quiver with relations βα=αβ=αn=βn=0.
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