Mixed Motives and Algebraic K-Theory

Crowdfunding has become a major consideration for individuals looking to fund their ideas, endeavors, and businesses. This phenomenon raises interesting questions for management scholars, such as what theories help to explain the nuance of crowdfunding as a form of entrepreneurial financing. With regard to what leads to crowdfunding campaign success, this chapter argues that there are mixed motives associated with contributing to these campaigns, and theoretical dynamics vary according to these different motives. The chapter also notes two fundamental differences of crowdfunding from more traditional means of funding early-stage ventures: the nature of engagement and preference toward product or person. Drawing on theory related to capabilities, the chapter identifies conditions under which crowdfunding is likely to be more and less advantageous based on these two dimensions. In summary, it provides a model that explains important sources of heterogeneity (i.e., motives) and homogeneity (i.e., diffused engagement and product lock-in) within the crowdfunding phenomenon that add nuance to theory in the entrepreneurial financing literature.

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Wilson loop algebras and quantum K-theory for Grassmannians

Journal of High Energy Physics ◽

10.1007/jhep10(2020)036 ◽

2020 ◽

Vol 2020 (10) ◽

Author(s):

Hans Jockers ◽

Peter Mayr ◽

Urmi Ninad ◽

Alexander Tabler

Keyword(s):

Wilson Loop ◽

Gauge Theories ◽

Wilson Line ◽

Quantum Cohomology ◽

Three Dimensional ◽

Loop Algebra ◽

Loop Algebras ◽

Verlinde Algebra ◽

K Theory ◽

Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

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A multiplicative K-theoretic model of Voevodsky’s motivic K-theory spectrum

Journal of Homotopy and Related Structures ◽

10.1007/s40062-018-0227-1 ◽

2018 ◽

Vol 14 (3) ◽

pp. 663-690

Author(s):

Youngsoo Kim

Keyword(s):

Theoretic Model ◽

K Theory

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Toward AGT for Parabolic Sheaves

International Mathematics Research Notices ◽

10.1093/imrn/rnaa308 ◽

2020 ◽

Author(s):

Andrei Neguţ

Keyword(s):

Field Theory ◽

Gauge Theory ◽

Conformal Field Theory ◽

Moduli Spaces ◽

Type A ◽

Conformal Field ◽

Toroidal Algebra ◽

Agt Correspondence ◽

K Theory ◽

The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

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