a new two step precoding strategy for closed loop mimo systems in this paper we present a new precoding technique using rotation transformations for closed loop multiple input multiple output mimo wireless systems which does not require the singular value decomposition svd operation of the channel transfer matrix and allows a simple maximum likelihood ml decoding at the receiver we divide the precoding process into two steps orthogonalization transformation which induces orthogonality between transmitted signals and beamforming transformation which achieves diversity gain in the proposed method we utilize a design criterion based on the minimum euclidean distance between the received signals and then the vector orthogonalization is connected to the vector norm maximization in this paper we focus on spatial multiplexing systems transmitting two independent data streams compared with the svd based schemes the proposed approach maintains a low complexity by relying only on three different kinds of rotation matrices for both the orthogonalization and beamforming transformation simulation results confirm that the proposed two step precoding achieves the better performance than the conventional svd based mimo precodings with reduced complexity

multiplicative preprojective algebras middle convolution and the deligne simpson problem abstract we introduce a family of algebras which are multiplicative analogues of preprojective algebras and their deformations as introduced by m p holland and the first author we show that these algebras provide a natural setting for the middle convolution operation introduced by n m katz in his book rigid local systems and put in an algebraic setting by m dettweiler and s reiter and h volklein we prove a homological formula relating the dimensions of hom and ext spaces study varieties of representations of multiplicative preprojective algebras and use these results to study simple representations we apply this work to the deligne simpson problem obtaining a sufficient and conjecturally necessary condition for the existence of an irreducible solution to the equation a 1 a 2 a k 1 with the a i in prescribed conjugacy classes in gl n c

cofree quiver settings abstract we give a complete classification of all quivers q and dimension vectors for which the representation space rep q is cofree as a representation of its natural symmetry group gl

middle convolution and harnad duality dettweiler reiter s additive description of katz s middle convolution can be interpreted in terms of the harnad duality using this interpretation together with mumford s geometric invariant theory we generalize the additive middle convolution to have a multi parameter and act on systems of linear ordinary differential equations with irregular singularities we show that the generalized operation holds basic properties of the original one and additionally show that katz s algorithm involving our generalization works well in generic case

some algorithms for semi invariants of quivers abstract we present some theorems and algorithms for calculating perpendicular categories and locally semi simple decompositions we implemented a computer program tetiva based on these algorithms and we offer this program for everybody s use

finitely presented simple modules over leavitt path algebras abstract let e be an arbitrary graph and k be any field we construct various classes of non isomorphic simple modules over the leavitt path algebra l k e induced by vertices which are infinite emitters closed paths which are exclusive cycles and paths which are infinite and call these simple modules chen modules it is shown that every primitive ideal of l k e can be realized as the annihilator ideal of some chen module our main result establishes the equivalence between a graph theoretic condition and various conditions concerning the structure of simple modules over l k e

qurves and quivers abstract in this paper we associate to a k qurve a formerly known as a quasi free algebra j cuntz d quillen algebra extensions and nonsingularity j amer math soc 8 1995 251 289 or formally smooth algebra m kontsevich a rosenberg noncommutative smooth spaces math ag 9812158 1998 the one quiver q 1 a and dimension vector 1 a this pair contains enough information to reconstruct for all n n the gl n etale local structure of the representation scheme rep n a in an appendix we indicate how one might extend this to qurves over non algebraically closed fields further we classify all finitely generated groups g such that the group algebra kg is a k qurve if char k 0 these are exactly the virtually free groups we determine the one quiver setting in this case and indicate how it can be used to study the finite dimensional representations of virtually free groups as this approach also applies to fundamental algebras of graphs of separable k algebras we state the results in this more general setting

noncommutative smoothness and coadjoint orbits abstract in math ag 0010030 math z to appear r bocklandt and the author proved that certain quotient varieties of representations of deformed preprojective algebras are coadjoint orbits for the necklace lie algebra n q of the corresponding quiver q a conjectural ring theoretical explanation of these results was given in terms of noncommutative smoothness in the sense of c procesi j algebra 107 1987 63 74 in this paper we prove these conjectures the main tool in the proof is the etale local description due to w crawley boevey math ag 0105247 along the way we determine the smooth locus of the marsden weinstein reductions for quiver representations

isomorphisms of quantizations via quantization of resolutions abstract in this paper we prove the existence of isomorphisms between certain non commutative algebras that are interesting from the representation theoretic perspective and arise as quantizations of certain poisson algebras we show that quantizations of kleinian singularities obtained by three different constructions are isomorphic to each other the constructions are via symplectic reflection algebras quantum hamiltonian reduction and w algebras next we prove that parabolic w algebras in type a are isomorphic to quantum hamiltonian reductions associated to quivers of type a finally we show that the symplectic reflection algebras for wreath products of the symmetric group and a kleinian group are isomorphic to certain quantum hamiltonian reductions our results involving w algebras are new while for those dealing with symplectic reflection algebras we just find new proofs a key ingredient in our proofs is the study of quantizations of symplectic resolutions of appropriate poisson varieties

a formal inverse to the cayley hamilton theorem abstract we prove that a q algebra r with formal trace can be realized as n n matrices if and only if it satisfies the cayley hamilton identity of degree n

necklace lie algebras and noncommutative symplectic geometry recently v ginzburg proved that calogero phase space is a coadjoint orbit for some infinite dimensional lie algebra coming from noncommutative symplectic geometry 12 in this note we generalize his argument to specific quotient varieties of representations of deformed preprojective algebras this result was also obtained independently by v ginzburg 13 using results of w crawley boevey and m holland 10 8 and 9 we give a combinatorial description of all the relevant couples alpha lambda which are coadjoint orbits we give a conjectural explanation for this coadjoint orbit result and relate it to different noncommutative notions of smoothness

generating graded central simple algebras abstract we solve the generator problem for z graded central simple algebras applications are given to automorphisms of trace rings of generic matrices and to periodic fat point modules

invariant theory of canonical algebras abstract based on the first fundamental theorem of classical invariant theory we present a reduction technique for computing relative invariants for quivers with relations this is applied to the invariant theory of canonical algebras and yields an explicit construction of the moduli spaces together with the quotient morphisms from the corresponding representation spaces for families of modules with a fixed dimension vector belonging to the central sincere separating subcategory by means of a tilting process we extend these results to the invariant theory of concealed canonical algebras thus covering the cases of tame hereditary tame concealed and tubular algebras respectively our approach yields in particular a uniform treatment to an essential part of the invariant theory of extended dynkin quivers a topic popular over the years but stretches far beyond since also concealed canonical algebras of tubular or wild representation type are covered

classes of degeneracy loci for quivers the thom polynomial point of view the chern classes for degeneracy loci of quivers are natural generalizations of the thom porteous giambelli formula suppose that e f are vector bundles over a manifold m and that s e f is a vector bundle homomorphism the question is which cohomology class is defined by the set6k s m consisting of points m where the linear map s m has corank k the answer due to i porteous is a determinant in terms of chern classes of the bundles e f we can generalize the question by giving more bundles over m and bundle maps among them the situation can be conveniently coded by an oriented graph called a quiver assigning vertices for bundles and arrows for maps we give a new method for calculating chern class formulae for degeneracy loci of quivers we show that for representation finite quivers this is a special case of the problem of calculating thom polynomials for group actions this allows us to apply a method for calculating thom polynomials developed by the authors the method reducing the calculations to solving a system of linear equations is quite different from the method of a buch and w fulton developed for calculating chern class formulae for degeneracy loci of a n quivers and it is more general can be applied to an dn e6 e7 and e8 quivers we provide sample calculations for a 3 and d4 quivers

connectedness of efficient solutions in multiple criteria combinatorial optimization abstract in multiple criteria optimization an important research topic is the topological structure of the set x e of efficient solutions of major interest is the connectedness of x e since it would allow the determination of xe without considering non efficient solutions in the process we review general results on the subject including the connectedness result for efficient solutions in multiple criteria linear programming this result can be used to derive a definition of connectedness for discrete optimization problems we present a counterexample to a previously stated result in this area namely that the set of efficient solutions of the shortest path problem is connected we will also show that connectedness does not hold for another important problem in discrete multiple criteria optimization the spanning tree problem

on the littlewood richardson polynomials we prove the equivalence of several descriptions of generators of rings of semiinvariants of quivers due to domokos and zubkov schofield and van den bergh and our earlier work we also show that the dimensions of semi invariants of weights n depend polynomially on n 2002 elsevier science usa all rights reserved

a proof of the popov conjecture for quivers abstract let q be a quiver with dimension vector we show that if the space of isomorphism classes of semisimple representations iss q of q of dimension vector is not smooth then the quotient map rep q iss q is not equidimensional in other words we prove the popov conjecture for the natural action of the linear reductive group gl on the space rep q of dimensional representations of the quiver q

hopf algebras with trace and representations we study the restriction of representations of cayley hamilton algebras to subalgebras this theory is applied to determine tensor products and branching rules for representations of quantum groups at roots of 1