On the Derived Category of the Cayley Plane
نویسنده
چکیده
We describe a maximal exceptional collection on the Cayley plane, the minimal homogeneous projective variety of E6. This collection consists in a sequence of 27 irreducible homogeneous bundles. 1. The Cayley plane Let O denote the normed algebra of (real) octonions (see e.g. [Ba]), and let O be its complexification. The space
منابع مشابه
Cayley graph associated to a semihypergroup
The purpose of this paper is the study of Cayley graph associated to a semihypergroup(or hypergroup). In this regards first we associate a Cayley graph to every semihypergroup and then we study theproperties of this graph, such as Hamiltonian cycles in this graph. Also, by some of examples we will illustrate the properties and behavior of these Cayley graphs, in particulars we show that ...
متن کاملOn the Derived Category of the Cayley Plane Ii
We find a full strongly exceptional collection for the Cayley plane OP, the simplest rational homogeneous space of the exceptional group E6. This collection, closely related to the one given by the second author in [Man11], consists of 27 vector bundles which are homogeneous for the group E6, and is a Lefschetz collection with respect to the minimal equivariant embedding of OP.
متن کاملOn the eigenvalues of normal edge-transitive Cayley graphs
A graph $Gamma$ is said to be vertex-transitive or edge- transitive if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$, respectively. Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$. Then, $Gamma$ is said to be normal edge-transitive, if $N_{Aut(Gamma)}(G)$ acts transitively on edges. In this paper, the eigenvalues of normal edge-tra...
متن کاملSOME GRAPH PARAMETERS ON THE COMPOSITE ORDER CAYLEY GRAPH
In this paper, the composite order Cayley graph Cay(G, S) is introduced, where G is a group and S is the set of all composite order elements of G. Some graph parameters such as diameter, girth, clique number, independence number, vertex chromatic number and domination number are calculated for the composite order Cayley graph of some certain groups. Moreover, the planarity of composite order Ca...
متن کاملOn the eigenvalues of Cayley graphs on generalized dihedral groups
Let $Gamma$ be a graph with adjacency eigenvalues $lambda_1leqlambda_2leqldotsleqlambda_n$. Then the energy of $Gamma$, a concept defined in 1978 by Gutman, is defined as $mathcal{E}(G)=sum_{i=1}^n|lambda_i|$. Also the Estrada index of $Gamma$, which is defined in 2000 by Ernesto Estrada, is defined as $EE(Gamma)=sum_{i=1}^ne^{lambda_i}$. In this paper, we compute the eigen...
متن کامل