<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        Questions tagged [homological-algebra]

        (Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.

        0
        votes
        0answers
        125 views

        Defining a graded ring structure on $\bigoplus_{i} \text{Ext}^i (A,A)$

        I read that, using the fact that $\text{Tot}^{\prod}(\text{Hom}(P_{\bullet} ,Q_{\bullet}))$ can by used to compute $\text{Ext}^* (A,B)$ (which I understand), we can give $\bigoplus_{i} \text{Ext}^i (A,...
        7
        votes
        1answer
        155 views

        Equivalence of definitions of Cohen-Macaulay type

        I know that the Cohen-Macaulay type has this two definitions: Let $(R,\mathfrak{m},k)$ be a Cohen-Macaulay (noetherian) local ring; $M$ a finite $R$-module of depth t. The number $r(M) = dim_k Ext_R^...
        2
        votes
        0answers
        106 views

        Milnor's conjecture on Lie group (co)homology and forgetful functor of extensions

        Let $G$ and $H$ be compact Lie groups, Consider $Ext_{Lie}(G,H)$ the set of isomorphism of extensions of Lie groups: $$ 1\rightarrow G\rightarrow M\rightarrow H\rightarrow 1 $$ There exists a ...
        2
        votes
        0answers
        33 views

        Hermitian structure for complexes of vector bundles

        Does it exist a different notion of Hermitian metric for complexes of vector bundles, besides the obvious data of a metric for each vector bundle? Same question for connections. In particular is there ...
        2
        votes
        1answer
        105 views

        How to check that exceptional sequence of vector bundles on Fano variety is helix foundation

        Let $X$ be smooth Fano variety with $\operatorname{Pic}(X) = \mathbb{Z}$ of dimension $m$ with canonical class $K$, and $E_0,...,E_n$ is exceptional sequence of $(n+1)$ vector bundles in $D^b(Coh(X))$....
        8
        votes
        2answers
        316 views

        Classification of algebras of finite global dimension via determinants of certain 0-1-matrices

        I restrict to the elementary problem that is equivalent to give a classification when Morita-Nakayama algebras have finite global dimension (see the end of this post for some background). A Morita-...
        6
        votes
        2answers
        155 views

        Derived invariance of the Cartan determinant

        The Cartan matrix $C$ of a finite quiver algebra $A$ with points $e_i$ is defined as the matrix having entries $c_{i,j}=\dim(e_i A e_j)$. The Cartan determinant is defined as the determinant of the ...
        3
        votes
        0answers
        103 views

        Injective resolution of the ring of entire functions

        Let $R$ be the ring of entire functions on $\mathbb{C}$. I heard that the concrete value of the global dimension of the ring depends on continuum hypothesis. I would think that the injective dimension ...
        7
        votes
        1answer
        134 views

        Gorenstein symmetric conjecture for arbitrary rings

        The Gorenstein symmetric conjecture states that for Artin algebras $A$ one has the the regular module has finite injective dimension as a right module if and only if it has finite injective dimension ...
        -1
        votes
        0answers
        64 views

        $(A[1])^{\otimes n}\backsimeq (A^{\otimes n})[n]$? [migrated]

        When $A$ is a $\mathbb{Z}$-graded module, $A[1]$ is the shift or suspension of $A$ (i.e $(A[1])^{i}=A^{i+1}$). May the $n$th power tensor of the shift be identified in this way?. Am I missing anything?...
        7
        votes
        0answers
        104 views

        homotopy MC element

        A homotopy MC element is the Linfty analog of a Maurer-Cartan element for a Lie algebra. Where is anything written about homotopy MC elements as perturbations of strict MC elements?
        2
        votes
        0answers
        82 views

        Singular homology: Lifting simplices gives map in homology

        Let $X$ be a space, $k=k_1+\dotsb+k_r$ and let $G:=\mathfrak{S}_{k_1}\times\dotsb\times \mathfrak{S}_{k_r}$ act freely on the right on $X$. Fix a commutative ring $R$ and another space $Y$. Then the ...
        6
        votes
        1answer
        150 views

        Explicit chain homotopy for the Alexander-Whitney, Eilenberg-Zilber pair

        Let $A$ and $B$ be simplicial abelian groups, and let $N_\ast(-)$ denote the normalized chain complex functor. Let $$AW_{A,B}\colon N_\ast(A\otimes B) \longrightarrow N_\ast(A)\otimes N_\ast(B)$$ and ...
        6
        votes
        1answer
        140 views

        Is the tensor product of pretriangulated dg-categories a pretriangulated dg-category?

        In "Grothendieck ring of pretriangulated categories", Bondal, Larsen and Lunts define a product of perfect (pretriangulated with Karoubian homotopy category) dg-categories as $A\bullet B:=Perf(A\...
        3
        votes
        0answers
        71 views

        Quartic link in a 5-sphere

        In this post I would like to propose a quartic link in a 5-sphere. Let us start with the following gluing into a 5-sphere: $$S^5=(D^2_{} \times T^3_{}) \cup_{T^4} ({S^5 \smallsetminus D^2 \times T^3})...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>