## Pairing in Group Cohomology [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for MathOverflow. Closed 5 years ago. Improve this question I am following Ararat Babakhanian’s Cohomological Methods in Group theory. Let A,B,C be G modules then we have a G module structre on HomZ(B,C) … Read more

## Ideals with certain properties

I recently isolated the following definition, which I believe it should have appeared somewhere. Let $\kappa$ be a cardinal, and let $X$ be a set with $\kappa^+\leq |X|$. Definition: An ideal $\mathcal I\subseteq \mathcal P(\mathcal P_{\kappa^+}(X))$ is called a B-ideal if the following hold. for every $x\in X$, $\{A\in \mathcal P_{\kappa^+}(X):x\in A \}$ is not … Read more

## Proof of Theorem 9.2 of the book Cubic Forms by Yu. I. Manin (end of page 37)

I warn that I first posted this question in Mathematics Stack Exchange but it got no attention at all. I think that it fits better there by its explanatory nature but maybe the book being reference is too advanced for that site. In the mentioned book there is some notation that it is not well … Read more

## What countable ordinals are called $\kappa_\alpha$?

Jervell has a notation for countable ordinals up to the small Veblen ordinal using trees: • Herman Ruge Jervell, How to wellorder finite trees and get good ordinal notations, Berkeley Logic Seminar, 3 October 2008. After illustrating this notation for various ordinals up to $\epsilon_0$ and $\epsilon_1$, on page 13 he illustrates it for two … Read more

## Why is there a discrepancy between the normalizations of the central terms for the commutation relations of the Virasoro versus Neveu-Schwarz Lie algebras?

Following the standard conventions in the literature, the commutation relations of the Virasoro Lie algebra are given by $$[L_m,L_n]=(m-n)L_{m+n}+\delta_{m,-n}\frac1{12}(m^3-m)c,$$ $$[c,L_n]=0.$$ Similarly, following the standard conventions in the literature, the commutation relations of the Neveu-Schwarz super Lie algebra are given by $$[L_m,L_n]=(m-n)L_{m+n}+\delta_{m,-n}\frac1{8}(m^3-m)c,$$ $$[J_\alpha,J_\beta]_ +=2L_{\alpha+\beta}+\delta_{\alpha,-\beta}\frac12(\alpha^2-\frac14)c,$$ $$[L_m,J_\alpha]=(\frac12m-\alpha)J_{m+\alpha},$$ $$[c,L_n]=0,\qquad [c,J_\alpha]=0.$$ The Virasoro algebra is a subalgebra of the Neveu-Schwarz … Read more

## Notation for upperbound power sets.

There is a standard notation $\mathrm{ZF}[n]$ for Zermelo Fraenkel set theory with the power set axiom restricted to saying the set of natural numbers has $n$ successive power sets $\beth_0\dots\beth_n$. Is there a similarly standard notation for the extension of $\mathrm{ZF}[n]$ by an axiom saying every set has an hereditary embedding in $\beth_n$? Answer In … Read more