Search results for "ideals"
showing 7 items of 17 documents
Tower sets and other configurations with the Cohen-Macaulay property
2014
Abstract Some well-known arithmetically Cohen–Macaulay configurations of linear varieties in P r as k-configurations, partial intersections and star configurations are generalized by introducing tower schemes. Tower schemes are reduced schemes that are a finite union of linear varieties whose support set is a suitable finite subset of Z + c called tower set. We prove that the tower schemes are arithmetically Cohen–Macaulay and we compute their Hilbert function in terms of their support. Afterwards, since even in codimension 2 not every arithmetically Cohen–Macaulay squarefree monomial ideal is the ideal of a tower scheme, we slightly extend this notion by defining generalized tower schemes …
Gradings on the algebra of upper triangular matrices of size three
2013
Abstract Let UT 3 ( F ) be the algebra of 3 × 3 upper triangular matrices over a field F . On UT 3 ( F ) , up to isomorphism, there are at most five non-trivial elementary gradings and we study the graded polynomial identities for such gradings. In case F is of characteristic zero we give a complete description of the space of multilinear graded identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . We finally compute the multiplicities in the graded cocharacter sequence for every elementary G -grading on UT 3 ( F ) .
ALGEBRE SIMMETRICHE DI ALCUNE CLASSI DI IDEALI MONOMIALI
The purpose of this thesis is the study of the symmetric algebra 〖Sym〗_S (L) of an interesting class of monomial ideals: the ideals L ⊂S=K[x1,...,xn,y1,...,ym] of mixed products in two sets of variables. Recently, this class is been used in order to test some algebraic conjecture, including the conjecture of Eisenbud -Goto, on the symmetric algebra 〖Sym〗_S (L) .Since such conjecture involves fundamental invariants of Sym (L), such as the Krull dimension, the multiplicity and regularity of Castelnuovo-Mumford, it was necessary to calculate these invariants or their bounds. This problem is difficult, but if L is generated by a s-sequence, you can arrive at a concrete result. In the work Mixed…
Varieties of algebras of polynomial growth
2008
Let V be a proper variety of associative algebras over a field F of characteristic zero. It is well-known that V can have polynomial or exponential growth and here we present some classification results of varieties of polynomial growth. In particular we classify all subvarieties of the varieties of almost polynomial growth, i.e., the subvarieties of var(G) and var(UT 2), where G is the Grassmann algebra and UT2 is the algebra of 2 x 2 upper triangular matrices.
Annihilators of tensor density modules
2007
Abstract We describe the two-sided ideals in the universal enveloping algebras of the Lie algebras of vector fields on the line and the circle which annihilate the tensor density modules. Both of these Lie algebras contain the projective subalgebra, a copy of sl 2 . The restrictions of the tensor density modules to this subalgebra are duals of Verma modules (of sl 2 ) for Vec ( R ) and principal series modules (of sl 2 ) for Vec ( S 1 ) . Thus our results are related to the well-known theorem of Duflo describing the annihilating ideals of Verma modules of reductive Lie algebras. We find that, in general, the annihilator of a tensor density module of Vec ( R ) or Vec ( S 1 ) is generated by …
A remark on hyperplane sections of rational normal scrolls
2017
We present algebraic and geometric arguments that give a complete classification of the rational normal scrolls that are hyperplane section of a given rational normal scrolls.