Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 11 of 11 for “"graded algebra"”.
-
Koszul duality for multigraded algebras
… the bounded derived category of complexes of graded modules over a graded algebra and the bounded derived category of complexes of graded modules over the quadratic dual graded algebra. This duality can be extended in many ways. We consider here two extensions: first we wish to allow a …
-
The Pure Virtual Braid Group is Quadratic
If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this thesis we give a sufficient …
-
K-theoretic Hall algebras for quivers with potential
… (Q, W), Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q, W). As shown by Davison-Meinhardt, this algebra comes with a filtration whose associated graded algebra is supercommutative. A special case of this construction is related to work of …
-
Invariants of Legendrian links
… is the powerful Chekanov-Eliashberg differential graded algebra, which we reformulate and generalize. We give applications to Legendrian knots and links in three-space and in the solid torus. A related question, the calculation of the maximal Thurston-Bennequin number for a link, is answered for …
-
Paramodular forms of degree 2 with particular emphasis on level t = 5
… goal of this thesis was to determine the algebraic structure of the graded algebra of all paramodular forms of degree 2 with level 5. A reduction process requires the calculation of the algebraic structure of a ring of modular forms with lower degree. As a main result of this thesis we …
-
Connections between Floer-type invariants and Morse-type invariants of Legendrian knots.
… rulings and the Chekanov-Eliashberg differential graded algebra: CE-DGA). Given a Legendrian knot $\sK$ with generic front projection $\sfront$, we define a combinatorial/algebraic object on $\sfront$ called a \emph{Morse complex sequence}, abbreviated MCS. An MCS encodes a finite sequence of …
-
Bordered Legendrian knots and sutured Legendrian invariants
… into several pieces, we associate a differential graded algebra to each "bordered" piece and prove a van Kampen theorem which recovers the Chekanov-Eliashberg invariant Ch(K) of the knot from the bordered DGAs. This leads to the construction of morphisms Ch(K) --> Ch(K') corresponding to certain …
-
Gröbner bases in rational homotopy theory
… bases, an analogue of Gröbner bases for free Lie algebras, to compute directly the E2 term for pushouts of wedges of spheres. In particular, for a cofiber sequence A --> X --> C where A and X are wedges of spheres, we use this calculations to generalize a result of Anick by giving necessary and …
-
Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
… complex) noncommutative and nonassociative algebras $\bbO_{p,q}$ (resp. $\bbO_{n}$) generalizing the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras. Introduced by Morier-Genoud and Ovsienko, these …
-
Polynomial Identities on Algebras with Actions
When an algebra is endowed with the additional structure of an action or a grading, one can often make striking conclusions about the algebra based on the properties of the structure-induced subspaces. For example, if A is an associative G-graded algebra such that the homogeneous component A1 …
-
Splines on polytopal complexes
This thesis concerns the algebra $C^r(\PC)$ of $C^r$ piecewise polynomial functions (splines) over a subdivision by convex polytopes $\PC$ of a domain $\Omega\subset\R^n$. Interest in this algebra arises in a wide variety of contexts, ranging from approximation theory and computer-aided geometric …