Monoidal Hom-Hopf algebras

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras and Lie algebras.Comment: 25 pages; extended version: compared to the version that appeared in Comm. Algebra, the Section Preliminary Results and Remarks 5.1 and 6.1 have been adde

Representations of hom-Lie algebras

In this paper, we study representations of hom-Lie algebras. In particular, the adjoint representation and the trivial representation of hom-Lie algebras are studied in detail. Derivations, deformations, central extensions and derivation extensions of hom-Lie algebras are also studied as an application.Comment: 16 pages, multiplicative and regular hom-Lie algebras are used, Algebra and Representation Theory, 15 (6) (2012), 1081-109

Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

Immigration Reforms as Health Policy

The 2020 election, uniting control of the political branches in the Democratic party, opened up a realistic possibility of immigration reform. Reform of the immigration system is long overdue, but in pursuing such reform, Congress should cast a broad net and recognize the health policies embedded in immigration laws. Some immigration laws undermine health policies designed to improve individual and population health. For example, immigration inadmissibility and deportability laws that chill noncitizens from enrolling in health-promoting public benefits contribute to health inequities in immigrant communities that spill over into the broader population—a fact highlighted by the still-raging COVID-19 pandemic. Restrictions on noncitizen eligibility for Medicaid and other public benefits contribute to inequitable access to health care. Moreover, visa restrictions for noncitizen health care professionals run counter to health policies promoting access to health care during a time of severe shortages in the health care professional workforce. It is time that health policy be incorporated into the immigration-reform debate, with Congress considering whether and how such reforms are helping to achieve health policy goals relating to improving individual and population health

A Pathway to Health Care Citizenship for DACA Beneficiaries

Since 2012, beneficiaries of Deferred Action for Childhood Arrivals (DACA) have enjoyed a certain normalization, however tenuous, of their status in the United States: they can legally work, their removal proceedings are deferred, and they cease to accrue unlawful presence. Regarding subsidized health coverage, however, DACA beneficiaries remain on the outside looking in. Although other deferred action beneficiaries are eligible for benefits through Medicaid, the Children’s Health Insurance Program, and the Affordable Care Act, the Obama Administration specifically excluded DACA beneficiaries. This decision undermines DACA’s goal of legitimizing beneficiaries’ presence in the United States. From a health policy perspective, it weakens efforts to improve health care equity, health care system efficiency, and public health. Changed circumstances in immigration and health policy justify a change in the policy excluding DACA beneficiaries from subsidized health coverage. It is no longer necessary to subordinate health-related interests to the decade-old, constrained choices of immigration policymakers. As a necessary stopgap on the way to immigration reform and health reform, the Biden Administration should eliminate the DACA carveout and extend the benefits of subsidized health coverage to all deferred action beneficiaries. The DACA carve-out is a useful case study illustrating how value-laden notions of deservingness in the laws governing eligibility for subsidized health care create systemic costs in the health care system and can harm public health

Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras

The purpose of this paper is to investigate ternary multiplications constructed from a binary multiplication, linear twisting maps and a trace function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie algebras starting from a binary multiplication of a Hom-Lie algebra and a trace function satisfying certain compatibility conditions involving twisting maps. We show that mutual position of kernels of twisting maps and the trace play important role in this context, and provide examples of Hom-Nambu-Lie algebras obtained using this construction

Immigration Reforms as Health Policy

The 2020 election, uniting control of the political branches in the Democratic party, opened up a realistic possibility of immigration reform. Reform of the immigration system is long overdue, but in pursuing such reform, Congress should cast a broad net and recognize the health policies embedded in immigration laws. Some immigration laws undermine health policies designed to improve individual and population health. For example, immigration inadmissibility and deportability laws that chill noncitizens from enrolling in health-promoting public benefits contribute to health inequities in immigrant communities that spill over into the broader population—a fact highlighted by the still-raging COVID-19 pandemic. Restrictions on noncitizen eligibility for Medicaid and other public benefits contribute to inequitable access to health care. Moreover, visa restrictions for noncitizen health care professionals run counter to health policies promoting access to health care during a time of severe shortages in the health care professional workforce. It is time that health policy be incorporated into the immigration-reform debate, with Congress considering whether and how such reforms are helping to achieve health policy goals relating to improving individual and population health