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Algebraic constructions in the category of vector bundles  [PDF]
Constantin M. Arcus
Mathematics , 2011,
Abstract: The category of generalized Lie algebroids is presented. We obtain an exterior di?erential calculus for generalized Lie algebroids. In particular, we obtain similar results with the classical and modern results for Lie algebroids. So, a new result of Maurer-Cartan type is presented. Supposing that any vector subbundle of the pullback vector bundle of a generalized Lie algebroid is called interior di?erential system (IDS) for that generalized Lie algebroid, a theorem of Cartan type is obtained. Extending the classical notion of exterior di?erential system (EDS) to generalized Lie algebroids, a theorem of Cartan type is obtained. Using the theory of linear connections of Ehresmann type presented in the paper [1], the identities of Cartan and Bianchi type are presented.
Equivariant vector bundles on Drinfeld's upper half space  [PDF]
Sascha Orlik
Mathematics , 2006,
Abstract: Let X be Drinfeld's upper half space of dimension d over a finite extension K of Q_p. We construct for every homogeneous vector bundle F on the projective space P^d a GL_{d+1}(K)-equivariant filtration by closed K-Frechet spaces on F(X). This gives rise by duality to a filtration by locally analytic GL_{d+1}(K)-representations on the strong dual. The graded pieces of this filtration are locally analytic induced representations from locally algebraic ones with respect to maximal parabolic subgroups. This paper generalizes the cases of the canonical bundle due to Schneider and Teitelbaum and that of the structure sheaf by Pohlkamp.
Tilting objects in the stable category of vector bundles on the weighted projective line of type (2,2,2,2;λ)  [PDF]
Jianmin Chen,Yanan Lin,Shiquan Ruan
Mathematics , 2013,
Abstract: We construct a tilting object for the stable category of vector bundles on a weighted projective line X of type (2,2,2,2;\lambda), consisting of five rank two bundles and one rank three bundle, whose endomorphism algebra is a canonical algebra associated with X of type (2,2,2,2).
Equivariant vector bundles, their derived category and $K$-theory on affine schemes  [PDF]
Amalendu Krishna,Charanya Ravi
Mathematics , 2014,
Abstract: Let $G$ be an affine group scheme over a noetherian commutative ring $R$. We show that every $G$-equivariant vector bundle on an affine toric scheme over $R$ with $G$-action is extended from $\Spec(R)$ for several cases of $R$ and $G$. We show that given two affine schemes with group scheme actions, an equivalence of the equivariant derived categories implies isomorphism of the equivariant $K$-theories as well as equivariant $K'$-theories.
On Double Vector Bundles  [PDF]
Zhuo Chen,Zhangju Liu,Yunhe Sheng
Mathematics , 2011,
Abstract: In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.
Meromorphic braided category arising in quantum affine algebras  [PDF]
Yan Soibelman
Physics , 1999,
Abstract: We construct a category of flat vector bundles on an elliptic curve. It arises in the representation theory of quantum affine algebras and carries meromorphic braided structure with singularities on the diagonal of the square of the curve.
A recollement of vector bundles  [PDF]
Xiao-Wu Chen
Mathematics , 2010, DOI: 10.1112/blms/bdr092
Abstract: For a weighted projective line, the stable category of its vector bundles modulo lines bundles has a natural triangulated structure. We prove that, for any positive integers $p, q, r$ and $r'$ with $r'\leq r$, there is an explicit recollement of the stable category of vector bundles on a weighted projective line of weight type $(p, q, r)$ relative to the ones on weighted projective lines of weight types $(p, q, r')$ and $(p, q, r-r'+1)$.
Homogeneous Vector Bundles on Symplectic Grassmannians  [PDF]
Martina Bode
Mathematics , 2012,
Abstract: In this paper the K-Theory and the category of homogeneous vector bundles on the symplectic Grassmannian SpGr(2,N) of isotropic 2-planes are discussed.
On the stratified vector bundles  [PDF]
Indranil Biswas
Mathematics , 2008,
Abstract: The stratified vector bundles on a smooth variety defined over an algebraically closed field $k$ form a neutral Tannakian category over $k$. We investigate the affine group--scheme corresponding to this neutral Tannakian category.
Canonical vector valued 1-forms on higher order adapted frame bundles over category of fibered squares
Anna Bednarska
Annales UMCS, Mathematica , 2008, DOI: 10.2478/v10062-008-0003-5
Abstract: Let Y be a fibered square of dimension (m1, m2, n1, n2). Let V be a finite dimensional vector space over. We describe all 21,m2,n1,n2 - canonical V -valued 1-form Θ TPrA (Y) → V on the r-th order adapted frame bundle PrA(Y).
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