Typically, a linear projection of the Grassmannian in its Plücker embedding is generically injective, unless image space. A notable exception are self-adjoint projections, which have even degree. We consider projections Gr3C6 with low-dimensional centers projection. When center has dimension less than five, we show that degree 1. five and greater 1, it self-adjoint.

In this article we investigate the relations between Gorenstein projective dimensions of [Formula: see text]-modules and their socles for text]-minimal Auslander–Gorenstein algebras text]. First give a description projective-injective in terms socles. Then prove that text]-module text] has dimension at most if only its socle is cogenerated by text]-module. Furthermore, show can be characterised...

In this paper we study a generalisation of the Igusa-Todorov functions which gives rise to vast class algebras satisfying finitistic dimension conjecture. This is called Lat-Igusa-Todorov and includes, among others, (defined by J. Wei) self-injective in general are not algebras. Finally, some applications developed theory given order relate different homological dimensions have been discussed t...

For a large class of metric spaces X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension dim(ν L X) of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X × R) = AN-asdim X + 1. We note that the similar equality for Gromov's asymptoti...

The paper is aimed at studying the topological dimension for sets definable in weakly o-minimal structures in order to prepare background for further investigation of groups, group actions and fields definable in the weakly o-minimal context. We prove that the topological dimension of a set definable in a weakly o-minimal structure is invariant under definable injective maps, strengthening an a...

In the first part of this paper the projective dimension of the structural modules in the BGG category O is studied. This dimension is computed for simple, standard and costandard modules. For tilting and injective modules an explicit conjecture relating the result to Lusztig’s a-function is formulated (and proved for type A). The second part deals with the extension algebra of Verma modules. I...

For an (n− 1)-Auslander algebra Λ with global dimension n, we give some necessary conditions for Λ admitting a maximal (n − 1)-orthogonal subcategory in terms of the properties of simple Λ-modules with projective dimension n − 1 or n. For an almost hereditary algebra Λ with global dimension 2, we prove that Λ admits a maximal 1orthogonal subcategory if and only if for any non-projective indecom...

We prove that in a 2-Calabi-Yau triangulated category, each cluster tilting subcategory is Gorenstein with all its finitely generated projectives of injective dimension at most one. We show that the stable category of its Cohen-Macaulay modules is 3-CalabiYau. We deduce in particular that cluster-tilted algebras are Gorenstein of dimension at most one, and hereditary if they are of finite globa...

In [Hov02], the second author introduced the Gorenstein projective and Gorenstein injective model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring. These two model structures are Quillen equivalent and in fact there is a third equivalent structure we introduce; the Gorenstein flat model structure. The homotopy category with respect to each of these is called the st...