User Adeek | chat.stackexchange.com

Adeek

Apr 24, 2020 13:33

www-users.math.umn.edu/~garrett/m/algebra/cech.pdf

Adeek

Apr 24, 2020 13:33

@Astyx here this is where I learned about all this stuff

Adeek

Apr 24, 2020 13:27

Sheaf cohomology is very useful

Adeek

Apr 24, 2020 13:26

you can compute sheaf cohomology for instance

Adeek

Apr 24, 2020 13:25

@Astyx what do you want to ask about sheaf cohomology ?

Adeek

Apr 24, 2020 13:23

@Astyx I can help you out I know about sheaf cohomology

Adeek

Apr 24, 2020 13:22

is it true that the commutant of U is proper subset of M ?

Adeek

Apr 24, 2020 13:22

let U be the set of all upper triangular matrices

Adeek

Apr 24, 2020 13:22

I think the commutant of 2x2 upper triangular matrices is subset of m ?

Adeek

Apr 24, 2020 13:21

yeah

Adeek

Apr 24, 2020 13:14

does anyone know whether upper triangular matrices are weak operator closed ?

Adeek

Apr 24, 2020 11:37

does anyone know the the bicommutant group of upper triangular matrices ?

Adeek

Mar 27, 2020 14:36

@AlessandroCodenotti where r u from btw ?

Adeek

Mar 27, 2020 14:36

@AlessandroCodenotti do you agree?

Adeek

Mar 27, 2020 14:35

Yeah I mean through this identification everything works out

Adeek

Mar 27, 2020 14:31

for H hilbert space

Adeek

Mar 27, 2020 14:30

you can identify nxn entries with elements in B(H) by Mn(H^n)

Adeek

Mar 27, 2020 14:25

I am pretty sure this is correct

Adeek

Mar 27, 2020 14:24

I want to ask let us say we have a net $(A_{\lambda}) in M_n(B(H)) = M_n(H^{n})$ for hilbert space H.
therefore the net A_lambda --> 0 iff a_i,j --> 0 for all i,j by identifying Mn(B(H)) with Mn(H^{n}) right?

Adeek

Mar 26, 2020 04:06

it is a simple question actually

Adeek

Mar 26, 2020 04:06

banach space ?

Adeek

Mar 26, 2020 04:05

hi @LeakyNun are you familiar with C* algebra?

Adeek

Aug 25, 2018 01:41

brb

Adeek

Aug 25, 2018 01:38

I always rely on my brain for everything

Adeek

Aug 25, 2018 01:38

what I am missing now @TedShifrin is some organizational skills.

Adeek

Aug 25, 2018 01:32

I have improved on that.

Adeek

Aug 25, 2018 01:31

the reason I covered a lot is because I wanted to be prepared for my PhD that is all.

Adeek

Aug 25, 2018 01:30

besides this is not PhD thesis it is just MSc thesis.

Adeek

Aug 25, 2018 01:30

just doing revisions atm

Adeek

Aug 25, 2018 01:30

I mean I am done already

Adeek

Aug 25, 2018 01:29

thx

Adeek

Aug 25, 2018 01:29

glad your enjoying your measure theory book.

Adeek

Aug 25, 2018 01:29

don't worry I mean I don't really take this personal it is okay

Adeek

Aug 25, 2018 01:28

yeah I will remove certain aspects of it.

Adeek

Aug 25, 2018 01:27

unless you have my thesis you can't say that.

Adeek

Aug 25, 2018 01:27

How do you know @DrewBrady ?

Adeek

Aug 25, 2018 01:26

yeah I agree

Adeek

Aug 25, 2018 01:25

yeah I agree.

Adeek

Aug 25, 2018 01:25

Yeah I mean my thesis is already 350 pages.

Adeek

Aug 25, 2018 01:23

yeah I will remove it

Adeek

Aug 25, 2018 01:23

your right

Adeek

Aug 25, 2018 01:23

yeah

Adeek

Aug 25, 2018 01:23

and I know the result which state that topological K-theory over X is the same as K-theory of coherent sheaves on X.

Adeek

Aug 25, 2018 01:22

$K_0(X)$ here being the K-theory of coherent sheaves on X.

Adeek

Aug 25, 2018 01:22

I know that G-R-R gives us somehow the isomorphism above. I don't know the details though.

Adeek

Aug 25, 2018 01:20

I don't know the details of the explicit isomorphisms involved.

Adeek

Aug 25, 2018 01:20

Grothiendieck-Riemann-Roch gives us $K_0(X) \otimes Q \cong A(X) \otimes Q$

Adeek

Aug 25, 2018 01:19

sorry adjusted.

Adeek

Aug 25, 2018 01:18

$K_0(X) \otimes Q \cong A(X) \otimes Q$

Adeek

Aug 25, 2018 01:18

Because of Grothiendieck-Riemann-Roch

Adeek

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