Derived autoequivalences from periodic algebras

We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by Rouquier-Zimmermann and is related to the autoequivalences of Seidel-Thomas and Huybrechts-Thomas. We show that compositions and inverses of these equivalences are controlled by the resolutions of our endomorphism algebra and that each autoequivalence can be obtained by certain compositions of derived equivalences between algebras which are in general not Morita equivalent.Comment: 34 pages; v2 is post referee report. The biggest changes from v1 are in Section 5.2. Final version has appeared in Proc. LM

Migratorial Disobedience: The Fetishization of Immigration Law

This short article lays the foundation for a theory of migratorial disobedience and explains how pro-border advocates fetishize immigration law

Professional Philosophy, “Diversity,” and Racist Exclusion: On Van Norden’s Taking Back Philosophy: A Multicultural Manifesto

A critical review essay, this work explains the methodological, material, and ideological reasons for why "diversity" initiatives in philosophy face an up-hill battle

Racism as Self-Love

In the United States today, much interpersonal racism is driven by corrupt forms of self-preservation. Drawing from Jean- Jacques Rousseau, I refer to this as self-love racism. The byproduct of socially-induced racial anxieties and perceived threats to one’s physical or social wellbeing, self-love racism is the protective attachment to the racialized dimensions of one’s social status, wealth, privilege, and/or identity. Examples include police officer related shootings of unarmed Black Americans, anti-immigrant sentiment, and the resurgence of unabashed white supremacy. This form of racism is defined less by the introduction of racism into the world and more on the perpetuation of racially unjust socioeconomic and political structures. My theory, therefore, works at the intersection of the interpersonal and structural by offering an account of moral complacency in racist social structures. My goal is to reorient the directionality of philosophical work on racism by questioning the sense of innocence at the core of white ways-of-being

Higher preprojective algebras, Koszul algebras, and superpotentials

In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting. We first show that the quiver of the higher preprojective algebra is obtained by adding arrows to the quiver of the original algebra, and these arrows can be read off from the last term of the bimodule resolution of the original algebra. In the Koszul case, we are able to obtain the new relations of the higher preprojective algebra by differentiating a superpotential and we show that when our original algebra is -hereditary, all the relations come from the superpotential. We then construct projective resolutions of all simple modules for the higher preprojective algebra of a -hereditary algebra. This allows us to recover various known homological properties of the higher preprojective algebras and to obtain a large class of almost Koszul dual pairs of algebras. We also show that when our original algebra is Koszul there is a natural map from the quadratic dual of the higher preprojective algebra to a graded trivial extension algebra

Output characteristics of tidal current power stations

With increasing targets being set for renewable-derived electricity generation, wind power is currently the preferred technology. It is widely accepted that due to the stochastic nature of wind, there is an upper limit to the capacity that can be accommodated within the electricity network before power quality is impeded. This paper demonstrates the potential of tidal energy as a predictable renewable technologies that can be developed for base load power generation and thus minimise the risk of compromising future power quality

Higher zigzag algebras

Given a Koszul algebra of finite global dimension we define its higher zigzag algeba as a twisted trivial extension of the Koszul dual. If our original algebra is the path algebra of a tree-type quiver, this construction recovers the zigzag algebras of Huerfano-Khovanov. We study examples of higher zigzag algebras coming from Iyama’s type A higher representation finite algebras, give their presentations by quivers and relations, and describe relations between spherical twists acting on their derived categories. We connect this to the McKay correspondence in higher dimensions: if G is a finite abelian subgroup of SLd+1 then these relations occur between spherical twists for G-equivariant sheaves on affine (d + 1)-space. 2010 Mathematics Subject Classification: 16. Associative rings and algebras; 18. Category theory, homological algebra; 14. Algebraic geometr

Serre functors and graded categories

We study Serre structures on categories enriched in pivotal monoidal categories, and apply this to study Serre structures on two types of graded k-linear categories: categories with group actions and categories with graded hom spaces. We check that Serre structures are preserved by taking orbit categories and skew group categories, and describe the relationship with graded Frobenius algebras. Using a formal version of Auslander-Reiten translations, we show that the derived category of a d-representation finite algebra is fractionally Calabi-Yau if and only if its preprojective algebra has a graded Nakayama automorphism of finite order. This connects various results in the literature and gives new examples of fractional Calabi-Yau algebras.Comment: 70 pages; v4 is post referee repor

What the Financial Services Industry Puts Together Let No Person Put Asunder: How the Gramm-Leach-Bliley Act Contributed to the 2008 - 2009 American Capital Markets Crisis

The current subprime financial crisis has shaped up to be one of the most dramatic and impactful events in the past few decades. No one particular factor fully accounts for why the American economy suffered setbacks unseen since the Great Depression of the 1930s. Some of the roots of the current financial crisis started taking hold in 1999 when Congress passed the Financial Services Modernization Act, also known as the Gramm-Leach-Bliley Act. Gramm-Leach-Bliley brought about sweeping deregulation to the financial services industry. In essence, Gramm -Leach-Bliley swept away almost six decades of financial services regulation precipitated by the Great Depression of the 1930s. Gram m-Leach-Bliley explicitly repealed the Glass-Steagall Act passed in the 1930s to stamp out much of the evil that caused the Great Depression. The year 2009 is a momentous year: it marks the ten-year anniversary of the passage of the Gramm-Leach-Bliley Act. This article posits that passage of the Gramm -Leach-Bliley Act in 1999, the Republican push for deregulation, and-most importantly repeal of the firewalls established by the Glass-Steagall Act accounts for why America is in the midst of one of the worst and deepest financial crises in our nation\u27s history. This article examines the Senate debates leading up to the passage of the Gramm-Leach-Bliley Act. Interestingly, a number of politicians issued powerful criticisms, predictions, and forecasts around the time of the passage of Gramm-Leach-Bliley that should have been taken seriously. Most notably, Senators Byron Dorgan (D-ND), Russell Feingold (D-WI), and Barbara Mikulski (D-MD) stood out as vocal critics. To gain further insight into the reach and effect of the Gramm-Leach-Bliley Act, this article examines the deregulatory effect of the legislation on two corporations in particular: Citigroup and Bank of America. This article then examines whether firewalls are necessary in the financial services industry. As the Troubled Asset Relief Program ( TARP ) has demonstrated, some institutions are too big to fail. This article explores what a return to Glass-Steagall regulation would do to prevent the too big to fail problem. Alternatively, it explores a three-tiered approach to financial services industry regulation. Finally, it explores whether we should let financial service industry institutions fail from a market efficiency standpoint, in the absence of strong regulation in the form of firewalls or stringent regulatory oversight