1
vote
0answers
93 views

Definition of 'Koszul Ring' (in BGS)

In the paper 'Koszul Duality Patterns in Representation Theory' by Beilinson et. al, they give the definition of a Koszul Ring: A Koszul ring is a positively graded ring $A = \bigoplus_{j \geq 0} ...
1
vote
0answers
236 views

Kunneth spectral sequence

In Rotman's Homological Algebra, 1st edition, there is written: Is every detail of 11.31-11.35 correct? Isn't the spectral sequence in 11.35 1st quadrant and not 3rd quadrant? Do 11.34-35 also ...
0
votes
2answers
304 views

An exercise about Tor [closed]

Let $I$ and $J$ be two ideals in $A$. Show that $\operatorname{Tor}_{1} (A/I, A/J) =\frac {I \cap J} { IJ} $ and $Tor_{2} (A/I, A/J) =\ker(I \otimes_ {A}J \to IJ )$. The first Tor is not a ...
5
votes
2answers
998 views

Algebraic Morse theory

In 2005, prof. Emil Skoldberg developed a theory, similar to Forman's Discrete Morse Theory, but suited for arbitrary based chain complexes, in his Morse Theory from an algebraic viewpoint. I'm going ...
5
votes
1answer
212 views

Hochschild homology and change of non-ground ring

Let $k$ be a field, $R$ is a commutative algebra over $k$ and $A$ is an associative algebra over $R$. There is a morphism of commutative algebras $R \to T$. Is it possible to reduce calculation of ...
2
votes
3answers
546 views

Are these Two Definitions of Quadratic Form (Algebraic, Topological) Related to Each Other?

Hi, All: I am trying to see if there is a nice relation between two different definitions of quadratic form q; a topological definition $q_T$, and an algebraic definition $q_A$, and, if there is, how ...
0
votes
1answer
136 views

Projectively splitting module

Is there a name for such class of modules $M$ such that $M\rightarrow N\rightarrow 0$ splits for every $N$ ?
3
votes
1answer
271 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, ...
3
votes
2answers
620 views

Injective modules and Pontrjagin duals

Forgive me for this naive question. We consider the following lemma and its proof in Lang's algebra, Third Ed., published 1999, Chap. 20, section 4, page 784. Every module is a submodule of an ...