Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComposition-Diamond Lemma for Modules
176
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we give some relationships among the Groebner-Shirshov bases in free associative algebras, free left modules and double-free left modules (free modules over a free algebra). We give the Chibrikovs Composition-Diamond lemma for modules and show that Kang-Lees Composition-Diamond lemma follows from this lemma. As applications, we also deal with highest weight module over the Lie algebra $sl_2$, Verma module over a Kac-Moody algebra, Verma module over Lie algebra of coefficients of a free conformal algebra and the universal enveloping module for a Sabinin algebra.
rate research
Read More
In this paper, we establish the Composition-Diamond lemma for free differential algebras. As applications, we give Groebner-Shirshov bases for free Lie-differential algebra and free commutative-differential algebra, respectively.
In this paper, we establish Composition-Diamond lemma for tensor product $k< X> otimes k< Y>$ of two free algebras over a field. As an application, we construct a Groebner-Shirshov basis in $k< X> otimes k< Y>$ by lifting a Groebner-Shirshov basis in $k[X] otimes k< Y>$, where $k[X]$ is a commutative algebra.
This paper shows how to obtain the key concepts and notations of Garside theory by using the Composition--Diamond lemma. We also show that in some cases the greedy normal form is exactly a Grobner--Shirshov normal form and a family of a left-cancellative category is a Garside family, if and only if a suitable set of reductions is confluent up to some congruence on words.
For an irreducible module $P$ over the Weyl algebra $mathcal{K}_n^+$ (resp. $mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $mathfrak{gl}_n$, using Shens monomorphism, we make $Potimes M$ into a module over the Witt algebra $W_n^+$ (resp. over $W_n$). We obtain the necessary and sufficient conditions for $Potimes M$ to be an irreducible module over $W_n^+$ (resp. $W_n$), and determine all submodules of $Potimes M$ when it is reducible. Thus we have constructed a large family of irreducible weight modules with many different weight supports and many irreducible non-weight modules over $W_n^+$ and $W_n$.
Morrison, Walker, and Wedrich used the blob complex to construct a generalization of Khovanov-Rozansky homology to links in the boundary of a 4-manifold. The degree zero part of their theory, called the skein lasagna module, admits an elementary definition in terms of certain diagrams in the 4-manifold. We give a description of the skein lasagna module for 4-manifolds without 1- and 3-handles, and present some explicit calculations for disk bundles over $S^2$.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
