on self injective algebras and standardly stratified algebras abstract the structure of a self injective algebra a which has a simple complement s such that the endomorphism algebra end a a s is standardly stratified is determined by giving its quiver and relations

a mackey imprimitivity theory for algebraic groups let g be an affine algebraic group over an algebraically closed field k and let h be a closed subgroup of g if v is a rational h module a comodule for the coordinate ring of h there is a now well known notion of an induced module vi g for g defined as the space morph g v of all h equivariant morphisms from g to a finite dimensional subspace of v with obvious g action the question arises given a rational g module m how can one recognize m as an induced module vig for a finite group g the answer is the mackey imprimitivity theorem the module m is induced if and only if it is a direct sum of subspaces permuted transitively by g with h the stabilizer of one of these subspaces called v one uses this result for example in proving the famous mackey decomposition theorem which describes the restriction of any induced module to a second subgroup l as a direct sum of suitable induced modules given the imprimitivity theorem the proof is just a matter of grouping the summands permuted by g into their orbits under l in the case of algebraic groups the situation is quite different for some subgroups h all g modules are induced this occurs for example if g is connected and k g h k e g if h is parabolic also if g is a connected unipotent group then a rational g module m is induced from some proper subgroup if and only if its endomorphism ring contains a two dimensional submodule e for the conjugation action of g with e k 1 and such that k l is precisely the subspace annihilated by the action of the lie algebra of g on e 27 cf also 5 5 below the latter is an application of a general criterion in case g h is affine a rational g module m is induced if and only if there is an action of the coordinate ring a of g h compatible with the action of g on both a and m note that this generalizes the imprimitivity theorem in the case of finite groups since then a has a k basis of g h orthogonal idempotents permuted transitively by g

randomization distributions and saddlepoint approximations in generalized linear models various randomization distributions are shown to arise as conditional distributions in the setting of generalized linear models these conditional distributions admit saddlepoint approximations which can obviate the need to simulate the randomization distributions they approximate examples include multinominal and dirichlet bootstraps the jackknife and permutation distributions the double saddlepoint approximation in a regular exponential family is shown to be equivalent to conditional use of a single saddlepoint approximation when the exponential family admits to a cut

a bocs theoretic characterization of gendo symmetric algebras abstract gendo symmetric algebras were recently introduced by fang and konig in 7 an algebra is called gendo symmetric in case it is isomorphic to the endomorphism ring of a generator over a finite dimensional symmetric algebra we show that a finite dimensional algebra a over a field k is gendo symmetric if and only if there is a bocs structure on a d a where d h o m k k is the natural duality assuming that a is gendo symmetric we show that the module category of the bocs a d a is equivalent to the module category of the algebra eae when e is an idempotent such that ea is the unique minimal faithful projective injective right a module we also prove some new results about gendo symmetric algebras using the theory of bocses

singular equivalences of functor categories via auslander buchweitz approximations abstract the aim of this paper is to construct singular equivalences between functor categories as a special case we show that there exists a singular equivalence arising from a cotilting module t namely the singularity category of t t and that of mod t are triangle equivalent in particular the canonical module over a commutative noetherian ring r induces a singular equivalence between cm r and mod r which generalizes matsui takahashi s theorem our result is based on a sufficient condition for an additive category a and its subcategory x so that the canonical inclusion x a induces a singular equivalence d sg a d sg x which is a functor category version of xiao wu chen s theorem

standardly stratified algebras and tilting abstract the concept of the characteristic tilting module and of the ringel dual for quasi hereditary algebras is generalized for the setting of standardly stratified algebras

the ariki terasoma yamada tensor space and the blob algebra we show that the ariki terasoma yamada tensor module and its permutation submodules m are modules for the blob algebra when the ariki koike algebra is a hecke algebra of type b we show that m and the standard modules have the same dimensions the same localization and similar restriction properties and are equal in the grothendieck group still we find that the universal property for fails for m making m and different modules in general finally we prove that m is isomorphic to the dual specht module for the ariki koike algebra

on a conjecture about dominant dimensions of algebras abstract we present examples of algebras a having dominant dimension n for every n 1 such that the algebra b end a i 0 n a has dominant dimension different from n where i 0 is the injective hull of a this gives a counterexample to a recent conjecture of chen and xi while the conjecture is false in general we show that a large class of algebras containing higher auslander algebras satisfies the conjecture

characteristic free representation theory of the general linear group on etudie systematiquement les z formes des representations rationnelles du groupe lineaire generale

on quantum spin chain spectra and the structure of hecke algebras and q groups at roots of unity we combine statistical mechanical and algebraic lie theory techniques to investigate the ordinary representation theory of the quotients of the hecke algebras when q is a root of unity we show how to determine the main invariants of these algebras the standard module contents of the indecomposable projective modules in general n we give complete explicit results in the cases n 2 3 these results are used to determine the q variation energy level convergences in invariant quantum spin chains

loewy series of certain indecomposable modules for frobenius subgroups we imitate some approaches in infinite dimensional representation theory of complex semisimple lie algebras by using the truncated category method in the categories of modules for certain frobenius subgroups of a semisimple algebraic group over an algebraically closed field of characteristic p 0 by studying the translation functors from p singular weights to p regular weights we obtain some results on l wy series of certain indecomposable modules

on the finitistic dimension conjecture iii related to the pair eae a let a be an artin algebra and e an idempotent element in a in this paper we use co homological conditions on a to control the finitistic dimension of eae such a consideration is of particular interest for understanding the finitistic dimension conjecture let us denote the finitistic dimension and global dimension of a by fin dim a and gl dim a respectively suppose gl dim a 4 then fin dim eae if one of the following conditions holds 1 a aea has representation dimension at most 3 2 a 3 a is an a aea module 3 proj dim sa 3 for all simple a aea modules s this result can be considered as a first step to the question of whether gl dim a 4 implies fin dim eae moreover we show the following let a be an arbitrary artin algebra and e an idempotent element of a such that the syzygy dimension or the gorenstein dimension of the eae module ae is finite if fin dim a then fin dim eae

homological theory of idempotent ideals let be an artin algebra u and a two sided ideal of then u is the trace of a projective module p in we study how the homological properties of the categories of finitely generated modules over the three rings u and the endomorphism ring of p are related we give some applications of the ideas developed in the paper to the study of quasi hereditary algebras

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

homological theory of recollements of abelian categories abstract we investigate several homological aspects of recollements of abelian categories in particular we study how various homological invariants and dimensions of the categories involved in a recollement situation are related and when recollements of abelian categories induce recollements at the level of the bounded derived categories finally we give applications to global finitistic and representation dimension of rings and artin algebras and to rouquier s dimension of triangulated categories

optimal consumption in a growth model with the cobb douglas production function an optimal consumption problem is studied in a growth model for the cobb douglas production function in a finite horizon the problem is transferred into a stochastic ramsey problem so as to reduce the dimension of the state space the corresponding state equation is a stochastic differential equation with inherently non lipschitz coefficients whose unique solvability is established the unique existence of the classical solution of the hamilton jacobi bellman equation associated with the original problem is proved and a synthesis of the optimal consumption policy is presented in the feedback form

optimal consumption of the finite time horizon ramsey problem abstract in this paper we study the stochastic ramsey problem related to an economic growth model with the ces production function in a finite time horizon by changing variables the hamilton jacobi bellman equation associated with this optimization problem is transformed by the viscosity solution technique we show the existence of a classical solution of the transformed hamilton jacobi bellman equation and then give an optimal consumption policy of the original problem

homological dimensions and strongly idempotent ideals abstract let a be an artin algebra and e an idempotent in a it is an interesting topic to compare the homological dimension of the algebras a a a e a and eae for example in 2 the relation among the global dimension of these algebras is discussed under the condition that aea is a strongly idempotent ideal motivated by this we try to compare the finitistic dimension of these algebras under certain homological conditions on aea in particular under the condition that aea is a strongly idempotent ideal with finite projective dimension we prove that if the finitistic projective or injective dimension of eae and a a e a are finite then the finitistic projective or injective dimension of a is finite this is a generalized version of the main result in 1

from submodule categories to the stable auslander algebra abstract we construct two functors from the submodule category of a representation finite self injective algebra to the module category of the stable auslander algebra of these functors factor through the module category of the auslander algebra of moreover they induce equivalences from the quotient categories of the submodule category modulo their respective kernels and said kernels have finitely many indecomposable objects up to isomorphism their construction uses a recollement of the module category of the auslander algebra induced by an idempotent and this recollement determines a characteristic tilting and cotilting module if is taken to be a nakayama algebra then said tilting and cotilting module is a characteristic tilting module of a quasi hereditary structure on the auslander algebra we prove that the self injective nakayama algebras are the only algebras with this property

general saddlepoint approximations of marginal densities and tail probabilities saddlepoint approximations of marginal densities and tail probabilities of general nonlinear statistics are derived these are based on the expansion of the statistic up to the second order their accuracy is shown in a variety of examples including logit and probit models and rank estimators for regression

saddlepoint approximations for marginal and conditional probabilities of transformed variables the lugannani and rice formula for tail areas in the univariate case has recently been extended to tail areas for marginal distributions and for conditional distributions in certain multivariate settings however the results on relative order of errors are given only formally or under the strong continuity assumptions necessary to obtain density approximations this paper attempts to give a unified treatment of these results for smooth transformations of multivariate means under weaker conditions appropriate to indirect edgeworth approximations for probabilities

enright s completions and injectively copresented modules let 21 be a finite dimensional simple lie algebra over the complex numbers it is shown that a module is complete or relatively complete in the sense of enright if and only if it is injectively copresented by certain injective modules in the bgg category o let a be the finite dimensional algebra associated to a block of o then the corresponding block of the category of complete modules is equivalent to the category of eae modules for a suitable choice of the idempotent e using this equivalence a very easy proof is given for deodhar s theorem also proved by bouaziz that completion functors satisfy braid relations the algebra eae is left properly and standardly stratified it satisfies a double centralizer property similar to soergel s combinatorial description of o its simple objects their characters and their multiplicities in projective or standard objects are determined

practical small sample asymptotics for regression problems abstract saddlepoint approximations are derived for sums of independent but not necessarily identically distributed random variables along with generalizations to estimating equations and multivariate problems these results are particularly useful for accurately approximating the distribution of regression coefficients general formulas are given for the distribution of the coefficients arising out of a generalized linear model with both canonical and noncanonical link functions we illustrate the case of logistic regression with a real data example and show how the gibbs sampler may be used to obtain confidence sets for each regression parameter based on the saddlepoint approximation

borelic pairs for stratified algebras abstract we determine all values of the parameters for which the cell modules form a standard system for a class of cellular diagram algebras including partition brauer walled brauer temperley lieb and jones algebras for this we develop and apply a general theory of finite dimensional algebras with borelic pairs the theory is also applied to give new uniform proofs of the cellular and quasi hereditary properties of the diagram algebras and to construct quasi hereditary 1 covers in the sense of rouquier with exact borel subalgebras in the sense of konig another application of the theory leads to a proof that auslander dlab ringel algebras admit exact borel subalgebras

on schur algebras and related algebras ii this paper is a continuation of 7 the purpose of 7 was to set up in the context of reductive algebraic groups a theory of generalized schur algebras a special case of our construction gives the schur algebras s n r studied extensively in lo we concentrate here on the schur algebras themselves and show that our construction yields new results in their representation theory by means of the schur functor see 10 chap 6 we obtain new results in the representation theory of the symmetric groups the main results are as follows the schur algebras s n r defined over a principal ideal domain r have finite global dimension see also 1 i over a field or complete valuation ring r every finitely generated projective s n r module has a weyl module filtration we prove the irreducibility of the socle of certain weyl modules see also 15 we describe a connection between weights of projective indecomposable modules for the schur algebras in terms of the involution on irreducible representations of symmetric groups given by tensoring with the sign representation we show that over a complete valuation ring or a field every young module for a symmetric group has a specht series in particular the projective indecomposables have specht series finally we show that for r n and a complete valuation ring or field r the blocks of the schur algebra s n r are given by the rule embodied in nakayama s conjecture the notations and conventions are as in the first part of this work 7

permutation complexes and modular representation theory hc g o iti has two basic functors a rg 2 di rh and a rh 2 rg given by restriction and induction which play an essential role in representation theory an important and elementary class of rg representations is permutation modules which are direct sums of modules indz r obtained by induction from the trivial rh module r for various hs g in another extreme one has rg modules which arise by induction from rh projective modules leading to the concept of relative projectivity and green s theory of vertices and sources cr gr the value of these subcategories of modules in representation theory and related areas is well known in a different direction influenced by algebraic geometry and topology one considers not only module categories but various categories of chain complexes of modules and their cohomologies this culminates in the more recent approaches to representation theory through the theory of derived categories see sc cps and their many references

the frobenius morphism in invariant theory abstract let r be the homogeneous coordinate ring of the grassmannian g gr 2 n defined over an algebraically closed field of characteristic p 0 in this paper we give a completely characteristic free description of the decomposition of r considered as a graded r p module into indecomposables frobenius summands as a corollary we obtain a similar decomposition for the frobenius pushforward of the structure sheaf of g and we obtain in particular that this pushforward is almost never a tilting bundle on the other hand we show that r provides a noncommutative resolution for r p when p n 2 generalizing a result known to be true for toric varieties in both the invariant theory and the geometric setting we observe that if the characteristic is not too small the frobenius summands do not depend on the characteristic in a suitable sense in the geometric setting this is an explicit version of a general result by bezrukavnikov and mirkovic on frobenius decompositions for partial flag varieties we are hopeful that it is an instance of a more general p uniformity principle

stratifying endomorphism algebras associated to hecke algebras abstract let g be a finite group of lie type and let k be a field of characteristic distinct from the defining characteristic of g in studying the non describing representation theory of g the endomorphism algebra s g k end kg j ind g p j k plays an increasingly important role in type a by work of dipper and james s g k identifies with a q schur algebra and so serves as a link between the representation theories of the finite general linear groups and certain quantum groups this paper presents the first systematic study of the structure and homological algebra of these algebras for g of arbitrary type because s g k has a reinterpretation as a hecke endomorphism algebra it may be analyzed using the theory of hecke algebras its structure turns out to involve new applications of kazhdan lusztig cell theory in the course of this work we prove two stratification conjectures about coxeter group representations made by e cline b parshall and l scott mem amer math soc 591 1996 and we formulate a new conjecture about the structure of s g k we verify this conjecture here in all rank 2 examples

quantum weyl reciprocity for cohomology we study the relationship between the cohomology of q schur algebras and hecke algebras in type a a key tool which has independent interest involves a specific hecke algebra resolution introduced in a special case by deodhar this resolution is somewhat akin to the koszul resolution for lie algebra cohomology in that it has an explicit description yet applies for all modules an application of the properties of this resolution establishes a quantum weyl reciprocity connecting in a range of degrees the cohomology of the q schur algebra with that of the hecke algebra this work also provides independently of the resolution cohomological inequalities which apply in all degrees and which sometimes can be related to kazhdan lusztig polynomials finally we extend to cohomology a decomposition number method of erdmann and illustrate its usefulness in computations this method enables us to exhibit some properties of symmetric group cohomology which if true would imply the sl n version of lusztig s characteristic p character conjecture

recollements and stratifying ideals abstract surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories these stratifying recollements are derived from recollements of module categories can every recollement be put in this form up to equivalence a negative answer will be given after providing a characterisation of recollements equivalent to stratifying ones moreover criteria for a ring epimorphism to be stratifying will be presented as well as constructions of such epimorphisms

analytical approximations to conditional distribution functions abstract conditional inference plays a central role in statistics but determination of relevant conditional distributions is often difficult we develop analytical procedures that are accurate and easy to apply for approximating conditional distribution functions for a continuous random vector we estimate conditional tail probabilities are smooth functions of x previous approaches have dealt with the cases where the variable whose conditional distribution is sought is a linear function of means and where there are p 1 conditioning variables however in many practical circumstances the statistic of interest is a nonlinear function of means and it is advantageous to condition on a lower dimensional ancillary statistic our procedure first involves approximating the marginal density function by an approach of phillips 1983 and tierney kass and kadane 1989 an accurate approximation to the required conditional probability is then obtained by applying a marginal tail probability approximation of diciccio and martin 1991 to the conditional density our method is illustrated in several examples including one which uses a saddlepoint approximation for the density of x and the method is applied for conditional bootstrap inference

optimal consumption models in economic growth abstract we study the optimal consumption problem in the one sector model of economic growth under uncertainty we show the existence of a classical solution of the hamilton jacobi bellman equation associated with the stochastic optimization problem and then give an optimal consumption policy in terms of its solution

tools for the symbolic computation of asymptotic expansions summary this paper describes a collection of procedures for the systematic computation of asymptotic expansions that are common in statistical theory and practice expansions of functions of sums of independent and identically distributed random variables the procedures permit the expansion of maximum likelihood estimates the associated deviance or drop in likelihood and more general functions of random variables with distributions involving one or more parameters the procedures are illustrated with examples involving general and specific laws much of statistical theory and practice is based on asymptotic expansions many programs are available to assist in the numerical evaluation of such expansions but there is a need for computational tools to assist in their derivation and symbolic evaluation heller 1991 shows how symbolic calculation may be used in a wide variety of statistical problems kendall 1988 1990 gives procedures for the symbolic computation of expressions in the analysis of the diffusion of euclidean shape silverman and young 1987 use computer algebra to evaluate criteria on which the decision to smooth a bootstrap distribution is based young and daniels 1990 apply symbolic computation to evaluate expressions in the assessment of bootstrap bias venables 1985 utilizes symbolic computation heavily to obtain expansions of maximum marginal likelihood estimates most notably fisher s a statistic barndorff nielsen and blasild 1986 describe procedures for the numerical calculation of bartlett factors in cases where cumulants of the likelihood function may be specified most of these references involve the evaluation of complicated formulae in particular cases and not the derivation of the formulae themselves here we give general procedures for both the derivation of formulae and their evaluation in specific cases the derivation of asymptotic expansions is typically a simple but laborious task consider for example the calculation of the expectation of the likelihood ratio test statistic for a one parameter family to order 1 n this may be accomplished in general

schur algebras of brauer algebras i a classical problem of invariant theory and of lie theory is to determine endomorphism rings of representations of classical groups for instance of tensor powers of the natural module schur weyl duality or of full direct sums of tensor products of exterior powers ringel duality in this article the endomorphism rings of full direct sums of tensor products of symmetric powers over symplectic and orthogonal groups are determined these are shown to be isomorphic to schur algebras of brauer algebras as defined in henke and koenig math z 272 3 4 729 759 2012 this implies structural properties of the endomorphism rings such as double centraliser properties quasi hereditary and a universal property as well as a classification of simple modules

a mckay correspondence for reflection groups we construct a noncommutative desingularization of the discriminant of a finite reflection group g as a quotient of the skew group ring a s g if g is generated by order 2 reflections then this quotient identifies with the endomorphism ring of the reflection arrangement a g viewed as a module over the coordinate ring sg of the discriminant of g this yields in particular a correspondence between the nontrivial irreducible representations of g to certain maximal cohen macaulay modules over the coordinate ring sg these maximal cohen macaulay modules are precisely the nonisomorphic direct summands of the coordinate ring of the reflection arrangement a g viewed as a module over sg we identify some of the corresponding matrix factorizations namely the so called logarithmic co residues of the discriminant

gorenstein defect categories of triangular matrix algebras abstract we apply the technique of recollement to study the gorenstein defect categories of triangular matrix algebras first we construct a left recollement of gorenstein defect categories for a triangular matrix algebra under some conditions using it we give a categorical interpretation of the gorenstein properties of the triangular matrix algebras obtained by x w chen b l xiong and p zhang respectively second under some additional conditions a recollement of gorenstein defect categories for a triangular matrix algebra is constructed as an application for a special kind of triangular matrix algebras which are called simple gluing algebras we describe their singularity categories and gorenstein defect categories

the modified signed likelihood statistic and saddlepoint approximations summary for a number of tests in exponential families we show that the use of a normal approximation to the modified signed likelihood ratio statistic r is equivalent to the use of a saddlepoint approximation this is also true in a large deviation region where the signed likelihood ratio statistic r is of order in

exchange property and the natural preorder between simple modules over semi artinian rings abstract we prove that if r is a right semi artinian ring then r is an exchange ring and every irredundant set simp r of representatives of simple right r modules carries a canonical structure of an artinian poset which is a morita invariant we investigate several basic features of this order structure and for a wide class of right semi artinian rings which we call nice we establish a link between those two sided ideals which are pure as left ideals and some upper subsets of simp r if r is nice and simp r does not contain infinite antichains then that link realizes an anti isomorphism from the lattice of upper subsets of simp r to the set of all ideals which are pure as left ideals further we show that every artinian poset possibly after adding a suitable maximal element if it is infinite is order isomorphic to simp r for some nice right semi artinian ring r

a conditional saddlepoint approximation for testing problems a saddlepoint approximation is provided for the distribution function of one m statistic conditional on another m statistic many interesting statistics based on dependent quantities e g spacings multinomial frequencies rank differences can be expressed in terms of independent identically distributed random variables conditioned on their sum so that this conditional saddlepoint approximation yields accurate approximations for the distribution of such statistics this saddlepoint approximation can also be used in conditional testing where nuisance parameters are eliminated by conditioning on sufficient statistics

homological epimorphisms recollements and hochschild cohomology with a conjecture by snashall solberg in view abstract we show that recollements of module categories give rise to homomorphisms between the associated hochschild cohomology algebras which preserve the strict gerstenhaber structure i e the cup product the graded lie bracket and the squaring map we review various long exact sequences in hochschild cohomology and apply our results in order to realise that the occurring maps preserve the strict gerstenhaber structure as well as a byproduct we generalise a known long exact cohomology sequence of koenig nagase to arbitrary surjective homological epimorphisms we use our observations to motivate and formulate a variation of the finite generation conjecture by snashall solberg

dominant dimension and idempotent ideals abstract let a be a finite dimensional algebra over a field k in this paper we study dominant dimension from the point of view of the idempotent ideals the canonical a bimodule v hom a d a a was studied in 8 11 9 where d hom k k under certain condition we give a new understanding that d a a v is isomorphic to an idempotent ideal tensor product itself as a bimodules and show that the double dual functor is defined by d a a v we also give a characterization of dominant dimension for a in terms of vanishing of certain extension groups over a which just uses a and da as ingredients and generalizes the corresponding characterizations given in 8 9 moreover we show that a is a motita algebra if and only if there is a natural isomorphism 1 on a mod where is the nakayama functor

on parameter transformations and interval estimation summary parameterizations which reduce the asymptotic bias and skewness of various pivotal quantities arising in large sample theory are discussed for models depending on an unknown scalar parameter transformation formulae by which such parameterizations can be obtained are derived and these formulae extend those for one dimensional curved exponential families given by hougaard 1982 to assess the accuracy of normal approximations to the distributions of the pivots their second order properties are considered and comparisons with the signed square root of the likelihood ratio statistic are drawn

strong exact borel subalgebras of quasi hereditary algebras and abstract kazhdan lusztig theory abstract strong exact borel subalgebras and strong subalgebras are shown to exist for quasi hereditary algebras which possess exact borel subalgebras and subalgebras this implies that the algebras associated with blocks of category o have strong exact borel subalgebras and strong subalgebras the structure of these subalgebras is shown to be closely related to abstract kazhdan lusztig theory the main technical tool in this paper is a construction which has an exact borel subalgebras of a given quasi hereditary algebra as input and a strong exact borel subalgebra as output from this result morita invariance of the existence of exact borel subalgebras is derived

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

realisation functors in tilting theory derived equivalences and t structures are closely related we use realisation functors associated to t structures in triangulated categories to establish a derived morita theory for abelian categories with a projective generator or an injective cogenerator for this purpose we develop a theory of non compact or large tilting and cotilting objects that generalises the preceding notions in the literature within the scope of derived morita theory for rings we show that under some assumptions the realisation functor is a derived tensor product this fact allows us to approach a problem by rickard on the shape of derived equivalences finally we apply the techniques of this new derived morita theory to show that a recollement of derived categories is a derived version of a recollement of abelian categories if and only if there are tilting or cotilting t structures glueing to a tilting or a cotilting t structure as a further application we answer a question by xi on a standard form for recollements of derived module categories for finite dimensional hereditary algebras