User Mahtab - Mathematics Stack Exchange

6 votes

1 answer

169 views

How many groups $G_i$ (up to isomorphism) are there such that $G\cong G_i \times \mathbb{Z}$?

asked Aug 19, 2023 at 13:39

6 votes

3 answers

313 views

Autocommutator subgroup is a characteristic subgroup

asked Jan 11 at 13:12

4 votes

2 answers

147 views

An example of a weakly Hopfian group which is not Hopfian

asked Jun 8, 2023 at 7:22

2 votes

1 answer

70 views

If $H$ is a proper retract of $G$ of finite homological type, then $\chi (H)\lneq \chi(G)$?

asked May 20, 2023 at 14:19

2 votes

1 answer

28 views

Definitions of polynomials $F(x):=f(x+c)$ and $G(x):=f(cx)$ if $c\in Z(R)$

asked Apr 4 at 13:19

2 votes

0 answers

37 views

Some confusion about $f_{p}$ when $f\in C^{\infty}(\mathfrak{g}^)$ and $p\in \mathfrak{g}^*$

asked Apr 12 at 11:01

2 votes

1 answer

102 views

The order of center of any non-abelian $p$-group of order $p^n$

asked Apr 19 at 14:43

2 votes

0 answers

20 views

A reference for the definition of a minimal polynomial when ring is noncommutative

asked May 8 at 3:39

2 votes

1 answer

60 views

About surjectivity of $V\cong (V^)^$

asked May 20 at 17:14

2 votes

1 answer

58 views

A question on geometric quantization

asked Jun 3 at 7:16

1 vote

1 answer

31 views

Momentum map for coadjoint orbit

asked Jun 4 at 6:04

1 vote

0 answers

22 views

Some details concerning projective representations in Wienberg's book

asked Jul 14 at 5:17

1 vote

1 answer

47 views

What does $\xi_{\mathcal{F}} -\langle \theta ,\xi_{\mathcal{F}}\rangle+\mathcal{F}$ mean?

asked May 23 at 12:28

1 vote

0 answers

24 views

Need some Help about understanding classifications of projective representations

asked May 24 at 14:00

1 vote

0 answers

44 views

Does every central extension come from a 2-cocycle?

asked May 12 at 12:13

1 vote

0 answers

23 views

How to see the vector field $[X,Y]$ as map $M\to TM$?

asked Apr 10 at 17:42

1 vote

1 answer

39 views

Some confusion in Kirillov-Kostant structure

asked Apr 11 at 4:12

1 vote

1 answer

43 views

In the decomposition of $G/Z(G)$ into direct product of cyclic groups at least two factors of maximal orders must accur?

asked Apr 20 at 13:37

1 vote

1 answer

90 views

Why $\phi_{*0}(\frac{d}{dt}|_0)=\frac{d\phi^{\mu}(t)}{dt}|_0\frac{\partial}{\partial g^{\mu}}|_e$?

asked Apr 10 at 13:45

1 vote

1 answer

36 views

Why any irreducible unitary representation of an abelian Lie group is one-dimensional?

asked Apr 1 at 5:23

1 vote

0 answers

34 views

Why these two representations are equivalent?

asked Apr 1 at 6:42

1 vote

0 answers

91 views

If $G$ is a simply connected Lie group and $H^2 (\mathfrak{g};\mathbb{R})=0$, then $H^2 (G;\mathbb{R})=0$?

asked Apr 2 at 13:33

1 vote

0 answers

92 views

Why $\mathbb{CP}^1 \cong S^2$? [closed]

asked Mar 5 at 13:16

1 vote

1 answer

57 views

Is every left ideal of $M_n (F)[x]$ principal?

asked Mar 11 at 13:57

1 vote

0 answers

54 views

Are these groups virtually polycyclic?

asked Jul 26, 2023 at 16:06

1 vote

0 answers

44 views

How to show this equality from the Cauchy integral formula

asked Sep 2, 2023 at 14:58

1 vote

1 answer

39 views

Why if $\chi (G)=k$, then we have $S(G,k)=\frac{P(G,k)}{k!}$?

asked Sep 9, 2023 at 16:46

1 vote

1 answer

41 views

What does this sentence mean in polynomial rings?

asked Feb 28 at 12:41

0 votes

1 answer

69 views

Lie algebra cohomlogy of $\mathbb{R}^2$

asked Mar 5 at 13:12

0 votes

1 answer

30 views

On IA-automorphism group

asked Jan 20 at 13:08

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61 Questions

How many groups $G_i$ (up to isomorphism) are there such that $G\cong G_i \times \mathbb{Z}$?

Autocommutator subgroup is a characteristic subgroup

An example of a weakly Hopfian group which is not Hopfian

If $H$ is a proper retract of $G$ of finite homological type, then $\chi (H)\lneq \chi(G)$?

Definitions of polynomials $F(x):=f(x+c)$ and $G(x):=f(cx)$ if $c\in Z(R)$

Some confusion about $f_{p}$ when $f\in C^{\infty}(\mathfrak{g}^)$ and $p\in \mathfrak{g}^*$

The order of center of any non-abelian $p$-group of order $p^n$

A reference for the definition of a minimal polynomial when ring is noncommutative

About surjectivity of $V\cong (V^)^$

A question on geometric quantization

Momentum map for coadjoint orbit

Some details concerning projective representations in Wienberg's book

What does $\xi_{\mathcal{F}} -\langle \theta ,\xi_{\mathcal{F}}\rangle+\mathcal{F}$ mean?

Need some Help about understanding classifications of projective representations

Does every central extension come from a 2-cocycle?

How to see the vector field $[X,Y]$ as map $M\to TM$?

Some confusion in Kirillov-Kostant structure

In the decomposition of $G/Z(G)$ into direct product of cyclic groups at least two factors of maximal orders must accur?

Why $\phi_{*0}(\frac{d}{dt}|_0)=\frac{d\phi^{\mu}(t)}{dt}|_0\frac{\partial}{\partial g^{\mu}}|_e$?

Why any irreducible unitary representation of an abelian Lie group is one-dimensional?

Why these two representations are equivalent?

If $G$ is a simply connected Lie group and $H^2 (\mathfrak{g};\mathbb{R})=0$, then $H^2 (G;\mathbb{R})=0$?

Why $\mathbb{CP}^1 \cong S^2$? [closed]

Is every left ideal of $M_n (F)[x]$ principal?

Are these groups virtually polycyclic?

How to show this equality from the Cauchy integral formula

Why if $\chi (G)=k$, then we have $S(G,k)=\frac{P(G,k)}{k!}$?

What does this sentence mean in polynomial rings?

Lie algebra cohomlogy of $\mathbb{R}^2$

On IA-automorphism group