All Questions
7 questions
28
votes
0
answers
527
views
What algebraic structure characterizes all natural operations between differential operators and differential forms?
On a smooth manifold $M$ one can define various algebraic structures, natural with respect to diffeomorphisms:
the differential graded-commutative algebra $\Omega(M)$ of differential forms on $M$;
...
- 37.8k
7
votes
1
answer
556
views
Quadratic algebras, quadratic operads, quadratic categories and quantum cohomology
Motivated by the quantisation of the symmetric laws in physics, the category of quadratic algebras has been endowed with two tensor products by Manin in his Montreal lectures notes. These products ...
- 3,652
7
votes
0
answers
460
views
Quantum polynomial rings and singularities
Something I've been thinking about lately has led me to wonder about the following. Consider the quantum polynomial ring $ Q= \mathbb{C}_{-1}[x_1,...x_n]$ generated as a graded ring in degree 1 with ...
- 3,758
5
votes
1
answer
129
views
Covariant splittings of Hopf algebra projections
What is an example of a pair of Hopf algebras $(A,B)$ with a surjective Hopf algebra map $\phi:A \to B$ such that $\phi$ does not admit a $B$-bi-comodule splitting $s:B \to A$? To be clear, the right $...
- 1,144
4
votes
1
answer
193
views
Quotient of quasi-isomorphic cdga's
I'm looking for a theorem about quotient of quasi-isomorphic cdga's:
Let $A, B$ be two cdga's (commutative differential $\mathbb Z$-graded algebra) of nonpositive degrees, and $\mathfrak m \subset A, ...
- 151
3
votes
1
answer
336
views
Why are relations of degree 3 or less enough in a presentation of the polynomial current Lie algebra g[t]?
Let $\mathfrak{g}$ be a finite dimensional simple Lie algebra over $\mathbb{C}$.
The polynomial current Lie algebra $\mathfrak{g}[t] = \mathfrak{g} \otimes \mathbb{C} [t]$
has the bracket
$$[xt^r, yt^...
- 138
3
votes
0
answers
53
views
Quotient of quasi-isomorphic nonpositively graded cdga's
I'm looking for a theorem about quotient of quasi-isomorphic cdga's:
Let $A, B$ be two cdga's (commutative differential $\mathbb Z$-graded algebra) concentrated in nonpositive degree, and $\mathfrak ...
- 151