Results 1  10
of
6,369
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
Abstract

Cited by 892 (13 self)
 Add to MetaCart
Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
An algebraic approach to network coding
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2003
"... We take a new look at the issue of network capacity. It is shown that network coding is an essential ingredient in achieving the capacity of a network. Building on recent work by Li et al., who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary n ..."
Abstract

Cited by 858 (88 self)
 Add to MetaCart
networks and robust networking. For networks which are restricted to using linear network codes, we find necessary and sufficient conditions for the feasibility of any given set of connections over a given network. We also consider the problem of network recovery for nonergodic link failures
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
Abstract

Cited by 1112 (21 self)
 Add to MetaCart
leader determination) for groups of discretetime agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i
Nested Linear/Lattice Codes for Structured Multiterminal Binning
, 2002
"... Network information theory promises high gains over simple pointtopoint communication techniques, at the cost of higher complexity. However, lack of structured coding schemes limited the practical application of these concepts so far. One of the basic elements of a network code is the binning sch ..."
Abstract

Cited by 345 (14 self)
 Add to MetaCart
proposed the idea of nested codes, or more specifically, nested paritycheck codes for the binary case and nested lattices in the continuous case. These ideas connect network information theory with the rich areas of linear codes and lattice codes, and have strong potential for practical applications. We
A lower bound on the essential dimension of a connected linear group
"... Let G be a connected linear algebraic group defined over an algebraically closed field k and H be a finite abelian subgroup of G whose order does not divide char(k). We show that the essential dimension of G is bounded from below by rank(H)−rank CG(H) 0, where rank CG(H) 0 denotes the rank of the m ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
Let G be a connected linear algebraic group defined over an algebraically closed field k and H be a finite abelian subgroup of G whose order does not divide char(k). We show that the essential dimension of G is bounded from below by rank(H)−rank CG(H) 0, where rank CG(H) 0 denotes the rank
LIE ALGEBRA INVARIANTS OF A FUNCTION ALGEBRA
, 2006
"... Summary. Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we correct and generalise a wellknown result about the Picard group of G. Then we prove that, if the derived group is simply connected and ..."
Abstract
 Add to MetaCart
Summary. Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we correct and generalise a wellknown result about the Picard group of G. Then we prove that, if the derived group is simply connected
Weak approximation and Manin group of Requivalences
, 1996
"... We extend one exact sequence of ColliotThélène and Sansuc for tori over number fields to one for arbitrary connected groups. 1 Introduction. Let G be a connected linear algebraic group defined over a number field k. Denote by ..."
Abstract
 Add to MetaCart
We extend one exact sequence of ColliotThélène and Sansuc for tori over number fields to one for arbitrary connected groups. 1 Introduction. Let G be a connected linear algebraic group defined over a number field k. Denote by
Affine Cones over Algebraic Varieties and Embeddings into Toric Prevarieties
, 2000
"... We introduce affine cones over not necessarily projective varieties and show that a variety admits such a cone if and only if it is divisorial. Moreover, we give an equivariant construction of affine cones. As an application, we obtain equivariant embeddability of normal divisorial varieties with ac ..."
Abstract
 Add to MetaCart
with action of a connected linear algebraic group into certain toric prevarieties.
ON THE CAYLEY DEGREE OF AN ALGEBRAIC GROUP
, 2006
"... Abstract. A connected linear algebraic group G is called a Cayley group if the Lie algebra of G endowed with the adjoint Gaction and the group variety of G endowed with the conjugation Gaction are birationally Gisomorphic. In particular, the classical Cayley map X ↦ → (In − X)(In + X) −1 between ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. A connected linear algebraic group G is called a Cayley group if the Lie algebra of G endowed with the adjoint Gaction and the group variety of G endowed with the conjugation Gaction are birationally Gisomorphic. In particular, the classical Cayley map X ↦ → (In − X)(In + X) −1 between
TWO ORBITS: WHEN IS ONE IN THE CLOSURE OF THE OTHER?
"... Abstract. Let G be a connected linear algebraic group, let V be a finite dimensional algebraic Gmodule, and let O1, O2 be two Gorbits in V. We describe a constructive way to find out whether or not O1 lies in the closure of O2. 1. ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract. Let G be a connected linear algebraic group, let V be a finite dimensional algebraic Gmodule, and let O1, O2 be two Gorbits in V. We describe a constructive way to find out whether or not O1 lies in the closure of O2. 1.
Results 1  10
of
6,369