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

Question about the notation $N_{\chi}(\alpha, T)$, the number of zeroes of the $L(s, \chi)$ in a rectangle

I am confused with what seems to be a standard notation in analytic number theory and I’d appreciate any clarification. I am interested in the zero density estimates, for example link.springer.com/article/10.1007/BF01403187 . In this paper and in many other sources I have seen, $N_{\chi}(\alpha, T)$ is defined to be the number of zeros of $L(s, … Read more

When is the Siegel-Walfisz theorem non-trivial?

The following paragraph appears in Analytic Number Theory (Iwaniec, Kowalski): The Siegel-Walfisz theorem asserts that: ψ(x;q,a)=xϕ(q)+O(x(logx)−A) for any q≥1,(a,q)=1,x≥2 and A≥0. Notice that this estimate is non-trivial only if q≪(logx)A. The last sentence is somewhat clear to me intuitively, and ought to answer my question. But I am not quite sure what Vinogradov’s ‘≪‘ notation … Read more

Standard notation/symbol for an embedding function

Hello everyone, Suppose that I am defining a function which embeds a surface (manifold) in R3. Is there a standard symbol or letter that is used for this function? Additionally, is there any other classical or standard notation (such as the hooked arrow for inclusion maps) of which I ought to be aware? Regards, Christopher … Read more

Terminology for metrics?

For some reason, I’m currently interested in the following relation – let $d,\delta$ be two metrics on some space $X$. We call the metrics _______ if there are some constants $C,E>0$ such that for all $x,y \in X$ $$ Cd(x,y)-E \le \delta(x,y) \le Cd(x,y)+E $$ I was looking for a proper adjective to put in … Read more