the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

triangulated categories and kac moody algebras by using the ringel hall algebra approach we find a lie algebra arising in each triangulated category with t 2 1 where t is the translation functor in particular the generic form of the lie algebras determined by the root categories the 2 period orbit categories of the derived categories of finite dimensional hereditary associative algebras gives a realization of all symmetrizable kac moody lie algebras

self dual manifolds with positive ricci curvature we prove that the connected sums cp2 cp2 and cp2 cp2 cp2 admit self dual metrics with positive ricci curvature moreover every self dual metric of positive scalar curvature on cp2 cp2 is conformal to a metric with positive ricci curvature supported in part by nsf grant dms 9204093

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway

root categories and simple lie algebras abstract by using the t 2 orbit category of the derived category of a hereditary algebra which is proved to be a triangulated category too we give a complete realization of a simple lie algebra this is a global version of ringel s work for the positive parts of simple lie algebras in this realization the grothendieck group provides the cartan subalgebra the indecomposable objects correspond to the chevalley basis and the structure constants are given by the evaluations of hall polynomials

triangulated categories of matrix factorizations for regular systems of weights with e 1 abstract we construct a full strongly exceptional collection in the triangulated category of graded matrix factorizations of a polynomial associated to a nondegenerate regular system of weights whose smallest exponents are equal to 1 in the associated grothendieck group the strongly exceptional collection defines a root basis of a generalized root system of sign l 0 2 and a coxeter element of finite order whose primitive eigenvector is a regular element in the expanded symmetric domain of type iv with respect to the weyl group

conformal deformations of integral pinched 3 manifolds abstract in this paper we prove that under an explicit integral pinching assumption between the l 2 norm of the ricci curvature and the l 2 norm of the scalar curvature a closed 3 manifold with positive scalar curvature admits a conformal metric of positive ricci curvature in particular using a result of hamilton this implies that the manifold is diffeomorphic to a quotient of s 3 the proof of the main result of the paper is based on ideas developed in an article by m gursky and j viaclovsky

regularity of a fourth order nonlinear pde with critical exponent in this paper we demonstrate the regularity of minimizers for a variational problem a special case of which arises in spectral theory and conformal geometry the associated euler lagrange equation is fourth order semilinear the leading term is the bilaplacian and lower order terms appear at critical powers

elliptic lie algebras and tubular algebras abstract this article is to study relations between tubular algebras of ringel and elliptic lie algebras in the sense of saito yoshii using the explicit structure of the derived categories of tubular algebras given by happel ringel we prove that the elliptic lie algebra of type d 4 1 1 e 6 1 1 e 7 1 1 or e 8 1 1 is isomorphic to the ringel hall lie algebra of the root category of the tubular algebra with the same type as a by product of our proof we obtain a chevalley basis of the elliptic lie algebra following indecomposable objects of the root category of the corresponding tubular algebra this can be viewed as an analogue of the frenkel malkin vybornov theorem in which they described a chevalley basis for each untwisted affine kac moody lie algebra by using indecomposable representations of the corresponding affine quiver

an equation of monge ampere type in conformal geometry and four manifolds of positive ricci curvature we formulate natural conformally invariant conditions on a 4 manifold for the existence of a metric whose schouten tensor satisfies a quadratic inequality this inequality implies that the eigenvalues of the ricci tensor are positively pinched

on borcherds type lie algebras for each even lattice mathcal l there is a canonical way to construct an infinite dimensional lie algebra via lattice vertex operator algebra theory we call this lie algebra and its subalgebras the borcherds type lie algebras associated to mathcal l in this paper we apply this construction to even lattices arising from representation theory of finite dimensional associative algebras this is motivated by the different realizations of kac moody algebras by borcherds using lattice vertex operators and by peng xiao using ringel hall algebras respectively for any finite dimensional algebra a of finite global dimension we associate a borcherds type lie algebra mathfrak bl a to a in contrast to the ringel hall lie algebra approach mathfrak bl a only depends on the symmetric euler form or tits form but not the full representation theory of a however our results show that for certain classes of finite dimensional algebras whose representation theory is controlled by the euler bilinear forms or tits forms their borcherds type lie algebras do have close relations with the representation theory of these algebras beyond the class of hereditary algebras these algebras include canonical algebras representation directed algebras and incidence algebras of finite prinjective types

vertex representations for n toroidal lie algebras and a generalization of the virasoro algebra vertex representations are obtained for toroidal lie algebras for any number of variables these representations afford representations of certainn variable generalizations of the virasoro algebra that are abelian extensions of the lie algebra of vector fields on a torus

the brill noether curve and prym tyurin varieties we prove that the jacobian of a general curve c of genus g 2a 1 with a ge 2 can be realized as a prym tyurin variety for the brill noether curve w 1 a 2 c as consequence of this result we are able to compute the class of the sum of secant divisors of the curve c embedded with a complete linear series g a 1 3a 2

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

on root categories of finite dimensional algebras abstract for any finite dimensional algebra a over a field k of finite global dimension we investigate the root category r a as the triangulated hull of the 2 periodic orbit category of a via the construction of b keller in on triangulated orbit categories this is motivated by ringel hall lie algebras associated to 2 periodic triangulated categories as an application we study the ringel hall lie algebras for a class of finite dimensional k algebras of global dimension 2 which turns out to give an alternative answer to a question of gim lie algebras by slodowy in beyond kac moody algebra and inside

hall algebras associated to triangulated categories by counting triangles and applying the octahedral axiom we find a direct way to prove the formula of toen in t section 5 1 for a triangulated category satisfying the left homological finiteness condition

recollement for differential graded algebras abstract a recollement of triangulated categories describes one such category as being glued together from two others this paper gives a precise criterion for the existence of a recollement of the derived category of a differential graded algebra in terms of two other such categories

matrix factorizations and representations of quivers ii type ade case abstract we study a triangulated category of graded matrix factorizations for a polynomial of type ade we show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding dynkin quiver also we discuss a special stability condition for the triangulated category in the sense of t bridgeland which is naturally defined by the grading