Forum Activity for @dariushaghababayeedehkordi

relative hyperhomology of modules

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hyperhomology of modules devoted to cartan -eilenberg

but relative hyperhomology even has not been worked

let T=Tot(KOY) s.t O=tensor product

if A is a sub total complex of T in this case there exist K_n_and Y_m

s.t A=Tot(K_nOY_m) we have exact sequence of relative Total complexes

---->Tot(K_0OY_0)----->Tot(KOY)----->(Tot(KOY),A)---->Tot(A)--->.....

with use of effect of Homology functor for above exact sequence we have following exact sequence :

----->H_n(Tot(K_nOY_m)---->H_n(Tot(KOY)----->H_n(T,A)----H_n-1(A)--->

now we provide that priliminaries for relative (co)hyperhomology two complex of sheavesand relative (co)homology of sheaves

with the best wishes darush.aghababayeedehkordi

updated by @dariushaghababayeedehkordi: 21/06/17 01:16:09PM

(co)homology of sheaf of modules with involution

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(co)homology of a sheaf of modules could be found in some geometry or algebraic topology books (for example reader can be refer to [Wa.rner]
but but we started (co)homology of sheaf of modules with involution :
let phi(L*) be a complex of sheaf of modules and A be a sheaf
in this case if gama(S) is a section of sheaf S on U in this case cohomology of this complex is H*(phi(S))=Z*(gama(phi(L*)OS)/B*(phi(L*)OS)). please inter your comment about it
with the best wishes
darush.aghababayeedehkordi

updated by @dariushaghababayeedehkordi: 21/06/17 01:16:09PM

hyperhomology of sheaves of modules with involution

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in previouse message please replace of moles with modules

in the body of title of this message

updated by @dariushaghababayeedehkordi: 21/06/17 01:16:09PM

hyper homology of sheaves of moles with involution

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let K * and L* are complexes of sheaves of modules with involution

s.t L is a resolution of Y

in this case we define hyper homology of sheaves of modules with involution is H_n(Gama(Tot(K*OY*)OS))

O =tensor product

is it true?

updated by @dariushaghababayeedehkordi: 21/06/17 01:16:09PM

n-ary sheaves

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A n-ary sheaf of n-ary K-modules consist of a topological space S together with a map pi from S to M satisfing the following conditions :

a)pi is a lo9cal n-ary homeomorphism of S toM

b)pi^-1(m) is a n-ary K-module for every m in M.

c)

composition laws are n-ary continuouse in topology on cartesina product of n-copies of S.

let SoSoS...S be the subspace of product of n-copies of S consist os all n-tuples (s_1,s_2,....,s_n) s-t pi(s_1)=pi(s_2)=.....=Pi(s_n).

the function f(s_1,s_2,...,s_n) =s_1-s_2+s_3-s_4+.....+s_n-1 -s_n of SoSoSo....oS to S be a n-ary continuouse

sheaves of n-ary K-algebras are defined similarly.

in aaxiom of C with additional property ( (s_1,s_2,...s_n)----> s_1s_2....s_n are n-ary continuouse.

n-ary presheaves will define in future.

darush.aghababayeedehkordi

updated by @dariushaghababayeedehkordi: 21/01/17 10:16:28PM

some questions about lie n-ary groups

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1: how do i define homomorphism between lie n-ary groups?

2: how do i define centre of a lie n-ary group ?

3: what is hypercentre of a lie n-ary group?

4: how do i define exponential mapon a lie n-ary groups?

5: how do i define lie n-ary algebra of a lie n-ary group?

6:how do idefine ad joint representation of a n-ary lie group?

updated by @dariushaghababayeedehkordi: 21/01/17 10:16:28PM

lie n-ary groups

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let G be a C -infinity manifold and there exist a c-infinity n-ary operation f from G cartesian G....G to G defined by f(x_1,x_2,....,x_n)=x_1x_2....x_n and generalized inverse is C -infinity

in this case G is called a lie n-ary groups or lie -multiary group or

lie lie -polyadic group.

updated by @dariushaghababayeedehkordi: 21/01/17 10:16:28PM