What was the relationship between the trends in African American politics and African American arts and culture during the late 1960s and early 1970s?

In the 1960s and 1970s, the relationship between African American politics and African American arts and culture was established through the Black Arts Movement, which began in 1965. In that year, the writer Larry Neal published an essay entitled "The Black Arts Movement." In that essay, which was a manifesto for the movement, he defined the Black Arts Movement as "the aesthetic and spiritual sister of the Black Power concept," a movement that "[proposed] a radical reordering of the Western cultural aesthetic." A year earlier, Neal established the Black Arts Repertory Theater in Harlem alongside fellow Black Arts Movement leader Amiri Baraka, a poet, essayist, and playwright formerly known as LeRoi Jones. Other key figures in this movement were Ishmael Reed (Mumbo Jumbo), Henry Dumas (Ark of Bones), the essayist and critic Addison Gayle Jr., and the poet Quincy Troupe.
Unfortunately, the most recognizable faces of the Black Arts Movement, like those of the Black Panther movement that coincided with it, were male. However, key women in the Black Arts Movement include Sonia Sanchez, Nikki Giovanni, and Audre Lorde (a vocal black lesbian feminist), whose political ambitions were expressed through their poetry. The female poets who sprang from Black Arts Movement ideology did not achieve prominence until the 1970s.
The Black Arts Movement began one year before Stokely Carmichael, then-leader of the Student Non-Violent Coordinating Committee (SNCC), gave his Black Power speech and one year before the formation of the Black Panther Party in Oakland, California—both of which occurred in 1966. The key connection between the Black Nationalist movement that the Black Panther Party pursued and the Black Arts Movement, which pursued a uniquely black aesthetic, was that both were interested in self-sufficiency. In this sense, they were perpetuating Booker T. Washington's view of self-determination and separation from the white community, as expressed in his Atlanta Compromise speech, while also embracing W.E.B. DuBois's avowal of political radicalism. Additionally, both proponents of the Black Arts Movement and those of the Black Panther Party wanted to create a cultural value system that was defined within the community. In this sense, these movements coincided with the decolonization movements that occurred in former colonies in West Africa and the Caribbean. Ideas were shared between black nationalists and decolonialist leaders—to wit, Stokely Carmichael was so inspired that he later changed his name to Kwame Touré, after both the first Ghanaian president Kwame Nkrumah and the Guinean leader Sekou Touré.
Finally, you shouldn't think that the 1960s saw the first confluence between arts and politics within the African American community. The Harlem Renaissance was not only a period of artistic flourishing but also a period in which black people pursued self-definition and political activism, particularly Marcus Garvey's repatriation movement through the United Negro Improvement Association (UNIA).