From a certain amount of Lie algebra theory (ultimately arising from an understanding of the behaviour of the exponential map on nilpotent matrices, and exploiting the hypothesis that is non-abelian) one can conclude that (after some initial preparations to avoid degenerate cases) must behave like...
This can be viewed as a rather complicated generalization of the following vaguely “cohomological”-looking observation: if one has some real numbers and some primes with for all , then one should have for some , where I am being vague here about what means (and why it might be useful ...
The tennis player problem is a microcosmic example of an abstract and pretty piece of mathematics. The example is bad because, although mathematicians are usually interested in things other than counting, it deals with counting; it's bad because it does not, cannot, exhibit any of the conceptua...
In contrast, we observe that, if we require that it be invariant under homological equivalence of differential coalgebras, there is no natural modeling of the comultiplication in the loop space. But, in rational homotopy theory, results of Milnor–Moore and Quillen show that there is a ...
This is the promised cohomological inter- pretation and generalisation of Proposition 1.2. Proposition 5.6. Let X be a geodesible vector field on a closed, oriented man- ifold M of dimension 2n + 1, and α a characteristic form for X. Then, volX = (−1)n[α]X • enX . If X...
26 Thomas Nikolaus Frobenius homomorphisms in higher algebra 44:56 Roman Mikhailov Homotopy patterns in group theory 43:16 Syu Kato The formal model of semi-infinite flag manifolds 45:16 Neena Gupta The Zariski Cancellation Problem and related problems in Affine Alge 40:01 Michael Larsen Character...
extending the algebra sheaf of smooth functions to a distribution-like algebra sheaf in which the former may be embedded, satisfying the pertinent cohomological conditions required for the coordinatization of all of the tensorial physical quantities, such that the form of the field equations is ...
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HOMOLOGICAL algebraVirtual resolutions are homological representations of finitely generated Pic(X)-graded modules over the Cox ring of a smooth projective toric variety. In this paper, we identify two algebraic conditions that characterize when a chain complex of graded free modules over the Cox ring...
Then the Stone dual of (i.e., the space of boolean homomorphisms ) is an extremally disconnected CH space. Proof: The CH properties are standard. The elements of give a basis of the topology given by the clopen sets . Because the Boolean algebra is complete, we see that the closure...